Papers

Sipser-Spielman codes and Dijkgraaf-Witten twisted gauge theories are among the most profound ideas in the last few decades in the areas of computer science and mathematical physics respectively. This work unifies them in the same framework using the language of sheaf cohomology, and produces a new framework of twisted sheaf gauge theories describing a class of quantum low-density parity-check (qLDPC) codes with non-Abelian $D_4$ topological order. The corresponding twisted Clifford-stabilizer qLDPC code can be obtained from gauging a new type of 0-form sub-complex symmetry from a qLDPC code defined on a general sheaf complex, and can be interpreted as a topological defect network of non-Abelian $D_4$ patches glued together with proper gapped interfaces. As an application, one can use this to realize a magic state fountain via the gauging measurement of the addressable logical CZ gates as 0-form subcomplex symmetries in a 2D hypergraph-product (HGP) sheaf code. This includes a scheme of subdividing an arbitrary constant-rate 2D HGP code with parameters $[[n,\Theta(n), \Omega(n^{1/2})]]$ into a quantum sheaf code which allows preparation of $\Theta(n^{1/2})$ logical CZ magic states in parallel, equivalent to the recent geometric construction using the code-to-manifold mapping in (arXiv:2601.06736). Moreover, using the recent sheaf complex and algebraic code constructions by Golowich-Tamo-Zhu (arXiv:2609.27801) with parameters $[[n,\Theta(n^{1-\epsilon}), \Omega(n^{(1-\epsilon)/2})]]$ for arbitrary small $\epsilon$, one can prepare $\Theta(n^{1-\epsilon})$ CZ magic states in parallel and hence achieve an almost-constant magic rate.

We study the spectrum of two-dimensional Yukawa theory using Hamiltonian truncation, with a focus on bound states. We extend the framework of Hamiltonian truncation effective theory to include fermions and logarithmic UV divergences. With these corrections, the energy levels converge as a function of the cutoff with the scaling predicted by power counting. We identify a strategy to follow the evolution of fermion-antifermion bound states from weak to strong coupling, and investigate its binding energy, finding good agreement with finite-volume perturbation theory at weak coupling. Finally, we explore the heavy-scalar regime toward the massive Thirring/Sine-Gordon limit, recovering the expected weak-coupling behavior and outlining how the calculation can be extended toward this limit.

Nonstabilizerness is a necessary resource for quantum systems to lie beyond the classically simulable regime. With the advent of stabilizer $\alpha$-Rényi entropies, nonstabilizerness has also become a many-body diagnostic, complementary to entanglement. While deciding whether an arbitrary quantum state has nonstabilizerness is provably hard, such states already require a description exponentially large in the number of qubits and are thus out of reach for many-body physics. Here we instead consider 2D tensor network (TN) states, which compactly capture states obeying an entanglement area law, and ask whether they admit a simpler algorithm for the same task. In contrast to the 1D case, we prove that, even at small, constant bond dimension, computing the stabilizer entropy of 2D TN states is $\#\mathrm{P}$-hard for any integer $\alpha\ge 2$, and deciding stabilizer membership is $\mathrm{C_=P}$-complete. The corresponding constant-accuracy problems remain $\mathrm{C_= P}$-hard. We further prove that deciding whether a PEPS can be transformed into a stabilizer state by local unitaries over a specified bipartition is $\mathrm{C_= P}$-hard. Under standard complexity assumptions, these results rule out classical or quantum algorithms with polynomial resources for all three tasks in the worst case.

In this work, we define $(3+1)$-dimensional topological quantum field theories (TQFTs) and their lattice realizations with input data given by a pivotal fusion 2-category; more precisely, our framework applies in wider generality to presemisimple locally fusion pivotal tensor $2$-categories, which are equipped with a so-called shadow trace. We introduce a decoration of triangulated manifolds by the input data, and develop a $20j$-symbol formalism for computing 4-simplex scattering amplitudes. We verify the topological invariance of 20$j$-symbol summations under the 4-dimensional Pachner moves. Furthermore, we also construct explicitly a 3-dimensional Levin-Wen-type lattice Hamiltonian model realizing the state-sum invariant. Our construction can be understood as a higher-dimensional analogue of the spin-networks construction for the Turaev-Viro invariant. Examples arising from $2$-groups are discussed from the perspective of higher gauge theory.

In a recent paper Nahum argued on the basis of a renormalization-group analysis that, contrary to standard lore, ground states of 1D spin chains with short-range interactions can spontaneously break U(1) “easy-plane” spin rotation symmetry. True long-range order of $(S^x,S^y)$ arises at the phase transition between two quasi-long-range-ordered phases. Here we present detailed numerical results for an anisotropic spin-1 chain model. We find a magnetization exponent $\beta\approx0.29$, consistent with the $\epsilon$-expansion prediction $\beta\approx0.28$, a divergence of the Luttinger parameter on approaching the transition from both sides with an exponent that we relate to Nahum's transition, and finite-size spectra consistent with a dynamical critical exponent $z\approx2$. Our results support the critical behavior predicted by Nahum's field theory.

To enable novel concepts in nanotechnologies, it is insightful to design materials with qualitatively new performances originating from recent discoveries in fundamental material science and physics. Curvilinear magnetism emerged as a tool to design chiral and anisotropic responses of materials at the nanoscale using the effects of the geometric shape and topology of the object. This concept is distinct yet complementary to material screening, which is primarily based on the optimization of intrinsic microscopic properties to modify magnetic textures for specific applications. Contemporary curvilinear magnetism focuses on mean-field micromagnetics, while the explicit contribution of the lattice structure and electronic degrees of freedom remains beyond consideration. In this review, we will emphasize on the effects which appear when this coupling is accounted for and that have resulted in novel concepts for the design of “metageometric” materials. Further development of this field will provide appealing technological prospects for fundamental understanding of curvilinear magnetic nanostructures and their applications in energy efficient and scalable nanoelectronics.

In atom-cavity systems, mean field theory is widely used, in which the quantum cavity operator is replaced by a classical amplitude. Then the problem is converted into atoms moving in a self-consistent potential. The mean field treatment captures the physics of cavity mediated interactions, and predicts the self-organized superradiant phase. In this work, however, we show that it fails for certain atom-cavity coupling: it predicts zero ground state atomic current where the fully quantum calculation exhibits a finite one. We find that the origin of this failure is the non-zero Berry curvature in the synthetic dimension spanned by the photon Fock ladder and real space. In this synthetic picture, the atomic current can be understood as Hall response of cavity detuning, whereas mean field collapses this dimension and discards the atom–photon correlations required for its Hall response. The same beyond-mean-field geometry predicts Laughlin-like photon generation under adiabatic flux insertion. Our work identifies synthetic Berry curvature as a concrete mechanism for the breakdown of static mean field in atom–cavity physics.

CeRh2As2 is a heavy-fermion superconductor that exhibits distinct low- and high-field superconducting phases, widely interpreted as reflecting a field-induced change in the parity of the order parameter. However, the superconductivity develops in close proximity to magnetic order whose microscopic origin and nature remain unclear. Moreover, the low-lying crystal-electric-field-split doublets of the Ce 4f electrons appear to realize an unusual "quasi-quartet" structure. This has motivated proposals that quadrupolar degrees of freedom play an important role in the low-temperature physics. Here we develop a microscopic heavy-fermion description of CeRh2As2 that incorporates both the quasi-quartet structure and the nonsymmorphic symmetry. Within a multiorbital periodic Anderson model, we include the lowest-lying $\Gamma_7$ and $\Gamma_6$ doublets of the Ce 4f electrons, and allow for nonlocal hybridization with the conduction d electrons. Single occupancy of the 4f states is enforced within the rotationally invariant slave-boson formalism. Adopting a mean-field treatment, we first show that the effective low-energy Hamiltonian is accurately captured by a single-orbital tight-binding model, justifying the minimal descriptions widely employed in the literature. Allowing for a magnetic ground state, we find that our model displays metallic $\mathbf{Q}=(\pi,\pi)$ antiferromagnetic order over a wide parameter regime. Ferromagnetic solutions also occur, but in a smaller region of parameter space and with greater sensitivity to carrier concentration and the form of the f-d hybridization. Quadrupolar moments appear only within magnetically ordered phases and are generally small, becoming substantial only when the $\Gamma_7$ and $\Gamma_6$ doublets are nearly degenerate. Our results provide a microscopic basis for understanding the itinerant heavy-fermion physics and ordered phases of CeRh2As2.

We investigated the crystal-electric-field (CEF) states in SmTr2Ge2 (Tr= Co-Cu and Ag) with the ThCr2Si2-type structure by magnetization and specific heat measurements. The magnetic anisotropy evolves systematically with Tr, changing from an easy ab plane for Tr = Co and Ni to an easy c axis for Tr = Cu and Ag. Combined analyses of the low-temperature susceptibility and magnetic entropy indicate a level crossing of the CEF ground state between Ni and Cu, together with a systematic evolution of the first excited CEF energy. The evolution of the magnetic properties correlates with changes in local structural parameters, providing an experimental basis for discussing how the ligand environment around the Sm ion is related to the 4f electronic state.

Moire superlattices in transition metal dichalcogenides provide a highly tunable platform for exploring strongly correlated electronic phases, such as generalized Wigner crystals. While these crystalline states typically melt with increasing thermal fluctuations, an electronic analogue of the Pomeranchuk effect can stabilize the localized solid phase at elevated temperature through isospin entropy. Here, we report the observation of an electronic Pomeranchuk effect at the fractional filling factors of $\nu = 1/3$ and $\nu = 1/4$ in AB-stacked twisted bilayer MoS$_2$ with twist angles of 4.1$^\circ$ and 3.9$^\circ$, respectively. At ultra-low temperature, the system exhibits a highly conducting, itinerant behavior at these fractional fillings, characteristic of a compressible Fermi-liquid ground state. Upon heating, the system exhibits a counterintuitive increase in the longitudinal resistivity, signaling an isospin-entropy-driven transition into a localized generalized Wigner crystal state. Our findings highlight the unique capacity of flat bands in twisted bilayer MoS$_2$ for stabilizing highly degenerate magnetic configurations, offering new insights into the thermodynamic phase diagrams of low-dimensional correlated systems.

The ground state, magnetization curves, low-temperature thermodynamics, and heat-engine performance of the fully frustrated spin-$1/2$ Heisenberg four-leg tube with antiferromagnetic inter- and intra-plaquette coupling constants J1 and J2 are examined using exact diagonalization, density matrix renormalization group, and localized-magnon theory. In the unfrustrated to weakly frustrated regime J2/J1 << 2, the system exhibits a continuous field-driven quantum phase transition between the gapped Haldane phase and a gapless Tomonaga-Luttinger quantum spin liquid. In the highly frustrated regime J2/J1 > 2, the system contrarily displays discontinuous field-driven quantum phase transitions between the Wigner magnon crystals, which are manifested in zero-temperature magnetization curves as intermediate plateaus at zero, one-quarter, one-half, and three-quarters of the saturation magnetization. The low-temperature magnetic and thermodynamic properties in this regime are accurately captured by an effective interacting lattice-gas model of two monomer quasi-particle species constructed from localized one- and two-magnon states. Finally, we explore a quantum Stirling heat engine using the fully frustrated four-leg tube as the working medium. The work output and efficiency are strongly suppressed near discontinuous field-induced transitions and reach pronounced local maxima well inside the stability regions of the Wigner magnon crystals.

We study the effects of zero-point spin fluctuations on the nuclear spin-lattice relaxation rate 1/$T_1$ around a two-dimensional antiferromagnetic quantum critical point in the self-consistent renormalization theory. For a weak mode-mode coupling constant $y_1 < $ 0.1, the finite temperature behavior of 1/$T_1$ across the quantum critical point resembles that for only the thermal spin fluctuations. For a strong mode-mode coupling constant $y_1 > $ 0.1, 1/$T_1$ takes its local maximum as a function of temperature in the nearly antiferromagnetic state. Experimental observation of the local maximum in the $^{63}$Cu nuclear spin-lattice relaxation rate 1/$T_1$ of lightly-doped superconductors La$_{2-x}$Sr$_x$CuO$_4$ with $x$ = 0.06-0.10 is associated with the effects of the zero-point spin fluctuations. The two-dimensional magnetic quantum critical point and the role of the zero-point spin fluctuations are discussed in the electron spin dynamics of underdoped superconductors La$_{2-x}$Sr$_x$CuO$_4$.

We consider a tunable hybrid device composed of four quantum dots and a floating superconducting island – the so-called poor man's tetron – close to its effective particle-hole symmetric point and coupled to four external leads. We predict the onset of a charge Kondo effect mediated by Cooper pairs, resulting from the strong crossed Andreev reflections that dominate its low-energy behavior. This two-channel Kondo effect makes the poor man's tetron behave as a double Cooper pair splitter, turning uncorrelated incoming electrons into spatially separated Cooper pairs. Based on renormalization group techniques, we analyze both its weak and strong coupling regimes and we determine its non-Fermi liquid signatures. Our estimates indicate that the fractional conductance and transport features associated to this two-channel charge Kondo effect can be observed over a broad range of temperatures and anisotropies in realistic experimental conditions.

Motivated by recent optical measurements in twisted MoTe$_2$ homobilayers, we numerically study the binding of itinerant anyons to ordinary electronic bound states. Using a minimal few-body model of an anyon alongside holes and electrons in a Gaussian trapping potential, we show that a fractionally charged bound state comprised of an anyon and an ordinary electronic trion can become favorable nearby local electrostatic defects. The resulting object is an anyonic molecule wherein the anyon is bound to the trion “nucleus,” which in turn is localized to the defect and can be excited optically. We find that the resulting anyon-trion can exhibit a photoluminescence red-shift relative to the ordinary trapped trion, with binding on the meV scale for parameters relevant to twisted MoTe$_2$. We find that the value of this red-shift depends on $\textit{both}$ the anyon's fractional charge and its kinetic energy, thereby encoding both universal and non-universal anyon properties. Our results are qualitatively consistent with observations in twisted MoTe$_2$.

Decoherence-induced phase transitions (DIPTs) are associated with singular changes in a quantum system's entanglement structure as the decoherence strength varies. In many cases, their critical strengths depend monotonically on the Rényi index of the entanglement diagnostic, forming a Rényi hierarchy. We identify a general mechanism for this hierarchy based on correlation inequalities in replicated statistical models that describe these DIPTs. We demonstrate it in $\mathbb{Z}_2$ topological stabilizer codes subject to independent phase-flip decoherence on each qubit and in a decohered rotor model with strong $\text{U}(1)$ symmetry. When the relevant correlations diagnose the DIPTs, these inequalities imply that the critical decoherence strength is nondecreasing with integer Rényi index $R\geq2$. We show that this mechanism also applies to a class of models with correlated decoherence.

There is disagreement in the literature concerning whether the nodal point of a three-dimensional Weyl semimetal survives weak short-range disorder: instanton calculations including fluctuations claim that the zero-energy density of states $\rho(0)$ vanishes, while exact numerics find a systematically finite number. We settle this disagreement with a full saddle-point calculation, including both instanton and fluctuations. Within the supersymmetric formulation for disorder, the instanton obeys a nonlinear Weyl equation whose solution is an exact $j=1/2$ hedgehog whose full functional form we numerically compute. We then compute the fluctuations about this saddle point, carefully identifying all zero modes, and computing the reduced superdeterminant as a convergent Fredholm determinant. No fermionic zero mode beyond a Kramers doublet exists, and at finite disorder $w$, the fluctuations become a finite one-loop prefactor, $\rho(0)=\mathcal{A} w^{-4} \exp(-s^*/w^2)(1+O(w^2))$, in normalized units with $s^* = 6.4163(2)$ and $\mathcal{A} = 27.47(8)$ for Gaussian-correlated disorder. This expression matches exact numerics on a single Weyl cone over four orders of magnitude with no fitted parameters (the amplitude is $\times 0.76$ the one-loop value), establishing that the density of states is finite for any disorder strength.

We study entanglement transitions for pairs of disjoint intervals in two-dimensional holographic interface conformal field theories. We consider several holographic models with equal central charges on the two sides of the interface: thin-wall geometries with one and two branes, the Janus solution, and the super-Janus solution. We first discuss the finite interface contribution to the entanglement entropy of a single interval, distinguishing intervals that cross the interface from those that lie entirely on one side. We then use the mutual information to locate the transition between connected and disconnected Ryu–Takayanagi geodesic configurations for two intervals. When the interface lies between the two intervals, increasing the boundary entropy $\log g$, which provides a measure of interface strength in the models considered here, generally decreases the critical separation at which the connected configuration ceases to dominate. When both intervals lie on the same side of the interface, the behavior is model dependent: the connected phase persists to larger separations in the Janus and super-Janus models, while the critical separation is unchanged in the thin-wall models. Thus, as diagnosed by the two-interval transition, the interface weakens correlations across the interface while preserving or enhancing correlations between regions on the same side. We also identify a universal “Silver Blaze” configuration, in which the interface lies inside one of the intervals and the transition occurs at the same location as in a CFT without an interface, independently of the interface parameters and of the holographic model. This universality follows from a cancellation between crossing and non-crossing interface contributions to the mutual information.

The observation of superconducting behaviour near a fractional Chern insulator in twisted MoTe$_2$ has sparked excitement about a possible direct "anyon superconducting" transition between a topologically ordered and a symmetry-broken phase. We carefully examine the experimentally measured transport data in the relevant region of the low-temperature tMoTe$_2$ phase diagram and propose a scenario where the nearby reentrant integer quantum Hall effect (RIQHE) acts as an intervening phase between the two. While the RIQHE is most prominent at large displacement fields, we propose that it extends to smaller fields at very low temperatures. Based on this picture, we model the sample as a patchwork of the three phases and show that such a model can explain the main qualitative features of the transport phase diagram, including its dependence on temperature and displacement field. The model predicts that at lower electronic temperatures the apparent FCI-SC transition at zero displacement field should split into two transitions separated by a narrow RIQHE region.

We demonstrate repulsion-driven topological superconductivity of a single species of Dirac fermions, motivated by valley-polarized phases observed in two-dimensional materials such as rhombohedral graphene. Using density-matrix renormalization group calculations on the Qi-Wu-Zhang lattice model on cylinders of width up to eight, we find a robust phase of spinless chiral $p$-wave superconductivity. Pairing already starts at low doping and thus occurs on a small, nearly isotropic Fermi pocket, and is therefore not tied to the particular details or anisotropy of the dispersion but instead seems tied to the non-trivial quantum geometry of the bands. In fact, the winding of the superconductor order parameter is opposite ("$p-ip$") to that of the anomalous Hall metal which forms the parent state, in agreement with expectations recently derived from weak coupling calculations. At larger doping, we find that a pair-density-wave component develops alongside zero-momentum pairing. Our work shows that the combination of strong repulsion, absence of time-reversal in the parent state, and non-trivial quantum geometry form a promising platform to realize topological superconductivity.

Commuting-projector Hamiltonians with integer spectrum such as the 1+1d Ising ferromagnet and the 2+1d toric code may be regarded as the generators of non-on-site $U(1)$ symmetries. In this paper we study whether these symmetries can be made on-site in the presence of finite and infinite-dimensional ancillae. In the finite-dimensional case, we prove that the fractionalized excitations, such as domain walls and anyons, make it impossible to on-site these Hamiltonians. On the other hand, we show that when infinite dimensional ancillae (e.g., rotors) are allowed, both the 1+1d Ising ferromagnet and the 2+1d toric code can be disentangled, yielding on-site symmetries. This is not in contradiction with the non-trivial ground state order of these Hamiltonians, since the ancilla Hamiltonians are no longer bounded from below. Our results indicate agreement between lattice and quantum field theory anomalies in the presence of infinite-dimensional ancillae, while with finite-dimensional ancillae the obstruction to on-siteability may even be non-invertible.

Renormalization group (RG) is a core concept in physics from statistical mechanics to quantum field theory, yet its schemes differ widely between field theory and many-body physics. We formulate the Wilsonian RG as a quantum channel, whose Kraus representation yields pure conditional trajectories for pure inputs and recovers mixed-state flows upon averaging. We then develop an algebraic extension applicable beyond the usual momentum-space, factorized setting: the low-energy algebra is constructed from the one-particle spectrum, and coarse graining is a conditional expectation onto it. We further construct a resource theory of RG whose free states are fixed points. For thermal states, the resulting relative-entropy monotone is proportional to $c-c_{\rm IR}$ to quadratic order along a single stable RG direction near a two-dimensional IR fixed point. We also introduce a complementary measure of the UV information discarded by coarse graining, establish its monotonicity for successive coarse-graining maps, and discuss its holographic realization.

Early string descriptions of doped antiferromagnets associate hole motion in a locally Néel ordered background with a path dependent antiferromagnetic string. We ask what becomes of this mechanism when long range Neel order is lost while short range antiferromagnetic correlations persist. The loss of long range order makes the projective RP^2 description admissible and opens a new topologically nontrivial sector. Its elementary defects are half vortices that globally minimize the RP^2 sigma-model energy within the nontrivial Z_2 sector. An a posteriori energetic comparison further shows why, once accessible, the projective director sector is favored over the corresponding vector reference texture. A pair of half vortices with opposite windings is logarithmically confined, V(R) = \kappa \ln\left(R/r_{\text{core}}\right), \kappa = \pi \rho_s /2. The resulting confinement is carried not by a one dimensional string but by an extended two dimensional spin texture. Thus, the loss of long range Néel order does not eliminate antiferromagnetic confinement but opens a distinct projective mechanism in which a local path dependent string is replaced, at long wavelengths, by a global topological texture with logarithmic confinement.

The Yukawa-Sachdev-Ye-Kitaev (YSYK) model, a solvable model of non-Fermi liquids with a proposed cavity-QED realization, couples $N$ complex fermions to $M$ bosons of frequency $\omega_0$ through random Yukawa couplings of strength $g$, and its dynamics depends only on $R\equiv\omega_0/g^{2/3}$. For $R\ll1$ the bosons are slow and act as a static random background in which the fermions are free, while for $R\gg1$ they are only virtually excited and generate a random four-fermion interaction of rank $M$, which is generically chaotic for $M\geq2$. Using exact diagonalization at infinite temperature, we follow the emergence of random-matrix statistics between these limits with unfolded spectral statistics and the Krylov complexity of the thermofield-double state. For complex couplings the level-spacing distribution evolves from Poisson to Gaussian-unitary-ensemble (GUE) statistics, the spectral form factor develops a correlation hole and a ramp, and the Krylov complexity evaluated on the unfolded spectrum develops a peak above its late-time plateau whose height reaches the GUE value. All diagnostics locate the onset around $R\approx0.3$, and adding boson modes moves it to smaller $R$. This delineates the parameter regime in which a cavity-QED realization would display random-matrix spectral correlations. On the other hand, real couplings give the same crossover towards Gaussian-orthogonal-ensemble (GOE) statistics, and along an interpolation between the two the peak height follows the mean gap ratio, so the peak identifies the symmetry class as well as the onset of chaos. Without unfolding the peak stays about 20$\%$ below its random-matrix value in both classes, which we trace to the non-semicircular density of states, and at larger $R$ the boson-number bands slow down the spreading of the state in Krylov space.

Weyl or Dirac fermions with the iconic linear energy-momentum relation and average density of states (ADOS) $\rho(E) \sim |E|^{d-1}$ at energy $E$ in $d$ spatial dimensions, constitute a unique setup to study the disorder-driven semimetal-to-metal quantum phase transition (QPT) between ballistic (realized for weak disorder) and diffusive (stabilized at stronger disorder) quasiparticles. Such a QPT takes place only for $d>2$ and falls beyond the realm of the Anderson metal-to-insulator transition. From numerically computed ADOS (using the kernel polynomial method) in dirty Weyl systems in $d=2$ to $6$, here we show that $d=2$ and $d=4$ are the lower ($d_\ell$) and upper ($d_u$) critical dimensions for such an unconventional QPT, respectively, as suggested from the solution of quasiparticle lifetime within the self-consistent Born approximation. Consequently, for $d \geq 4$ the associated correlation length exponent is found to be $\nu \approx 0.5$ (within numerical accuracy). However, the dynamic scaling exponent at the quantum critical point is pinned close to $z \approx d/2$ (numerically) for any $d \geq 3$, which is shown to be an exact result from a field-theoretic renormalization group calculation. Therefore, Weyl semimetal-to-metal QPTs can be studied field theoretically around both $d_\ell$ and $d_u$.

Moiré superlattices assembled by twisting Bernal and rhombohedral multilayer graphene host a rich set of interaction-driven magnetic and topological states, yet superconductivity has not been observed in these systems except in proximity to a transition-metal dichalcogenide. Here we report incipient superconductivity and tunable Chern insulators in twisted bilayer-trilayer graphene encapsulated by hexagonal boron nitride. Across twist angles from $\theta = 1.05^\circ$ to $1.50^\circ$, Chern insulators form at integer and fractional moiré fillings for electron doping, with Chern numbers up to |C| = 3 set by twist angle and tuned by doping. At $\theta = 1.18^\circ$, a symmetry-broken metallic region forms for hole doping and hosts a trivial insulator at band filling $\nu = -2$. Displacement field alone drives this insulator into a pocket of incipient superconductivity with a sharp transition, a well-defined critical current, and a critical temperature that peaks near the insulating boundary, although the resistance does not fall to zero. In-plane magnetic field expands the pocket, which persists to more than four times the weak-coupling Pauli limit, and stabilizes a second pocket in which Fraunhofer-like modulation of the critical current signals phase-coherent pairing. Twisted bilayer-trilayer graphene thus offers a single gate-tunable system in which pairing can be interfaced with Chern insulators whose topology is itself an adjustable parameter.

We study the spin-1/2 nearest-neighbor Heisenberg model on the breathing pyrochlore lattice in the mixed ferro-antiferromagnetic regime, where one tetrahedral sublattice is antiferromagnetic and the other ferromagnetic. The classical ground-state manifold is then that of the nearest-neighbor face-centered-cubic (fcc) antiferromagnet built from composite tetrahedral moments. Classical Monte Carlo simulations and the self-consistent Gaussian approximation show that thermal order-by-disorder lifts its subextensive degeneracy and selects the collinear Type-I state with wave vector $X=(1,0,0)$ through a strongly first-order transition. Pseudofermion functional renormalization group calculations for $S=1/2$ and $S=1$ reveal a nonmagnetic window adjacent to the decoupled antiferromagnetic-tetrahedron limit, beyond which $X$ order reappears. Density matrix renormalization group calculations show that this window is not featureless: the antiferromagnetic tetrahedra develop nearly ideal tetramer correlations, with four bonds carrying $\langle\mathbf{S}_i\cdot\mathbf{S}_j\rangle\simeq-1/2$ and the two opposite bonds $\simeq+1/4$, while the structure factor retains broad maxima at $X$. A third-order effective Hamiltonian in the tetrahedral-singlet manifold explains this: reversing the sign of the inter-tetrahedron coupling converts Tsunetsugu's dimer selection into a uniform tetramer selection, as confirmed by exact diagonalization. A dynamic high-temperature expansion traces how local tetrahedral excitations give way to low-energy $X$-centered spectral weight. Finally, we place density-functional parameters for eight structures of spin-3/2 breathing chromium thiospinels in the classical phase diagram. The mapping reproduces the $\mathbf{k}=(1,0,0)$ order of CuInCr$_4$S$_8$, accounts for the absence of order in LiGaCr$_4$S$_8$, and predicts Type-I order for LiInCr$_4$S$_8$.

The topological order of the Kitaev toric code is insensitive to disorder in its couplings since all star and plaquette operators commute; consequently, the stabilizer ground-state manifold is independent of the individual coupling strengths, and the phase remains stable against weak local perturbations. This insensitivity, however, is a property of the eigenstates and not of the dynamics they generate, and we show that the disorder sensitivity of a probe prepared outside that eigenbasis can be a metrological resource. In particular, we investigate the estimation of the strength of three topological-order-breaking perturbations, the nonlinear Castelnovo-Chamon deformation, nearest-neighbor Ising interactions, and a magnetic field along horizontal edges, encoded on an initially separable probe through unitary evolution under the disordered toric code Hamiltonian. We demonstrate that the quenched average quantum Fisher information (QFI), a figure of merit for metrological precision, exceeds that of its ordered counterpart in suitable regimes of perturbation strength and encoding time. For the ordered case, we further identify optimal product probes, for which the quadratic and cubic terms of the short-time expansion vanish identically, leaving a transient quartic scaling of QFI. Interestingly, this window persists as long as the multipartite entanglement generated by the encoding continues to increase, and it survives under local dephasing, bit-flip, and amplitude damping noise acting independently on each site, with the non-unital channel being the least detrimental.

Characterizing carrier type in strongly correlated quantum systems conventionally relies on the Hall effect. In cold-atom quantum simulators, implementing Hall transport measurements typically requires synthetic gauge fields, which introduces significant heating. Here, we present nonlinear spectroscopic and fluctuation-based protocols that establish an alternative route to identifying the sign of quasiparticle charge. We demonstrate that second-order density and current responses to finite-momentum quenches and drives-as well as equilibrium third-order density cumulants-distinguish electron- from hole-like quasiparticles. For a Fermi-Hubbard multi-leg ladder on a square lattice, numerical simulations reveal a crossover from hole- to electron-like carriers upon hole-doping away from half-filling, matching the sign change in the Hall coefficient. To demonstrate the applicability of our protocols beyond fermionic systems, we show that the nonlinear density response to a finite-momentum, finite-frequency drive reveals the sign of charge carriers in a hard-core boson ladder, and that the nonlinear signal can be significantly enhanced when driving near resonance with a nonlinear collective mode. Our results establish nonlinear density and current response and equilibrium non-Gaussian fluctuations as complementary probes, offering quantum simulators a direct route to characterize the carrier sign, without the experimental hurdles of conventional transport setups.

We introduce a class of tensor-network states in which physical legs are shared among local tensors, termed leg-tied tensor ansätze (LETTA). Physical leg ties encode long-range correlations directly, while a virtual matrix product state (MPS) backbone retains short-range multipartite entanglement. The linear virtual backbone allows us to develop a deterministic density matrix renormalization group-like variational optimization algorithm using exact contractions over the active tie-boundary sets and local minimization. We demonstrate the advantages of LETTA for the two-dimensional frustrated $J_1$–$J_2$ Heisenberg model and the three-dimensional transverse-field Ising model. Our results show that LETTA is substantially more accurate than same-bond-dimension MPS calculations and can typically reach the accuracy of much larger MPS calculations using one order of magnitude fewer variational parameters. LETTA thus opens the door for explicitly correlated tensor-network states that can encode long-range correlation beyond virtual bonds.

For normal PEPS, the fundamental theorem settles at the finite level whether virtual-bond gauge exhausts a tensor network's representation freedom. We ask the first-order question at a fixed representation, from both sides of the differential: which tensor variations leave the state unchanged without being bond gauges, and which physical directions can no variation reach? We answer both exactly for weighted graph state (WGS) tensor networks with equal physical and bond dimension $q\ge2$, which include the graph-state resources of measurement-based quantum computation. Dividing a single-tensor variation by the nonvanishing amplitude turns it into an arbitrary function on the closed neighborhood of its vertex. Overlapping neighborhoods give the complete kernel. Its non-bond part is generated on periodic regular-polygon tilings by triangles, chordless squares, and edge-sharing diamonds. Under stated period conditions, generic gauge completeness on all thirty-nine families studied identifies this nullity as a WGS rank drop: for thirty-three families at every $q\ge2$, and for six at $q=2$. Supports outside every neighborhood give the missing directions: at qubit graph states on the eleven Archimedean tilings every nearest-neighbor $XX$ and $YY$ direction is missing, including on honeycomb, where the non-bond kernel is empty. On large honeycomb and square tori, small nonzero coherent $XX$ errors leave the bond-two PEPS set on the same graph. Removing redundant parameters and supplying missing directions are therefore distinct operations.