Papers

Photoemission spectroscopy on high $T_c$ superconductors find a puzzling nodal self-energy with $\omega/T$ scaling and an exponent varying continuously with doping. We propose a mechanism: nonlocality induced by poorly screened effective repulsions $V_{\alpha}(r) \sim 1/r^\alpha$, where a continuously doping-dependent exponent $1 \le \alpha \le 3$ interpolates between the Mott insulating and Fermi liquid limits. We develop a phenomenology of hydrodynamic screening, finding a scale-covariant quasiparticle decay rate $\Gamma(\omega,T) \propto T^{\gamma} \Phi(\omega/T)$ in energy $\omega$ and temperature $T$, with $\gamma = 2-\frac{1}{\alpha}$ for nonlocal $ 1 < \alpha < 2$. Our results naturally capture the optimally doped to overdoped regimes, whereas the underdoped regime is qualitatively distinct. In our theory, spectroscopy-fitted exponents directly probe the charged fluid's effective spatial nonlocality, providing a way to falsify the theory by comparing photoemission spectroscopy against electron energy loss spectroscopy. More broadly, nonlocality cautions us to not immediately infer quantum critical phenomena when $\omega/T$ scaling is experimentally observed.

In low density systems with strong interactions electrons are expected to crystallize into a Wigner solid. Recently, advances in two-dimensional systems where electrons carry Berry curvature have added a topological dimension to Wigner crystallization. Using a model for pseudospin interactions in a topological Wigner crystal, here we show that the competition between ferromagnetic Heisenberg exchange $J$ and the chiral interaction $\gamma$ on the triangular lattice stabilizes a zero-field skyrmion crystal whose density is continuously tunable through the ratio $\gamma/J$. The chiral interaction originates from finite Berry curvature in an underlying time-reversal broken Wigner crystal. In the continuum limit, the chiral interaction acts as a chemical potential for skyrmions, while higher-order gradient terms beyond the nonlinear sigma model select the skyrmion density. At large chiral coupling, we uncover a 24-site tetra-skyrmion crystal carrying four units of topological charge per magnetic unit cell, which becomes degenerate with four-sublattice tetrahedral order as $J \to 0$. We characterize the magnon structure for these phases and discuss the transition between the tunable skyrmion crystal to these states at large $\gamma/J$. Our results establish the phase diagram of ferromagnetic topological Wigner crystals.

Understanding how a parent insulating state shapes the superconductivity that emerges upon doping is a long-standing problem dating back to Anderson's resonating-valence-bond proposal. The triangular-lattice Hofstadter-Hubbard model with $\pi/2$ flux per plaquette offers an ideal setting: at half filling it hosts two distinct parent states—an integer quantum Hall insulator and a chiral spin liquid—separated by a topological phase transition. Using neural quantum states on tori of up to $432$ sites, we present strong evidence that the transition is continuous, with a vanishing $2e$ charge gap and critical charge fluctuations. Upon doping, we find a topological superconductor on either side of the transition. While the pairing order parameter remains nearly unchanged across the transition, the superfluid stiffness is strongly enhanced near the critical point. The energy scale of the superconductor is therefore set not by which parent state is doped, but by proximity to the transition between them. Our results establish neural quantum states as a powerful tool for understanding the interplay between unconventional electronic correlations and superconductivity.

Equipped with the recently recognized symmetry structure of mixed states of matter and "strong-weak spontaneous symmetry breaking" (SW-SSB), we develop a quantum particle-vortex duality of emergent model-F and model-A hydrodynamics of 2d boson/rotor systems. This duality relation demonstrates that classical hydrodynamics of 2d bosons can be described in terms of the charge symmetry $U(1)_c$, but also equivalently in terms of the dual (emergent) 1-form symmetry $U(1)^{(1)}_e$, as well as $U(1)_v$ associated with the conservation of vortices. This duality provides a bridge between the hydrodynamics of matter and magnetohydrodynamics.

We present a fermionic lattice Hamiltonian that exactly realizes the $\mathrm{U(1)}_\mathrm{L}\times \mathrm{U(1)}_\mathrm{R}$ global symmetry and the associated chiral anomalies of a massless Dirac fermion in 1+1 dimensions. The construction couples Villain bosons to a Kitaev chain of Majorana fermions, where the bosonic fields are essential for evading Nielsen-Ninomiya-type no-go theorems. For two copies of our model, we realize the anomaly-free $\mathrm{U(1)}_{3450}$ global symmetry and construct symmetric boundary conditions. We analytically demonstrate symmetric mass generation by mapping the symmetry-preserving six-fermion interactions to fermion bilinear terms using fermionic T-duality. Finally, by gauging general anomaly-free global symmetries, we obtain a broad class of lattice chiral gauge theories. As nontrivial applications, we compute the mass spectra of the lattice Schwinger model and the 3450 gauge theory, finding agreement with the corresponding continuum results.

Recent experiments in moiré materials have enabled the realization of a variety of exotic quantum phases. In this context, the Hofstadter-Hubbard model has been proposed as a possible setting for hosting chiral spin liquid. Concurrently, significant progress has been recently made in the computational methods for two-dimensional many-body fermion systems, which makes numerically studying this challenging model a real possibility in genuine 2D geometry. Motivated by these advances, we investigate the putative chiral spin liquid phase in the triangular-lattice Hofstadter-Hubbard model using variational Monte Carlo with neural quantum states (NQS) and projected entangled pair states (PEPS). We observe spin-charge separation directly in real space through numerical spin-pumping simulation and real-time spin and charge motion. In addition, in the context of anyonic superconductivity conjectured in this model, we find a positive two-electron binding energy on small systems, but it decreases below our numerical resolution as the system size increases. Our work demonstrates NQS and PEPS as powerful tools, capable of cross-checking each other, for diagnosing topological order and fractionalized excitations in strongly correlated electronic systems.

Tensor network methods provide powerful analytical and numerical tools for characterizing quantum phases of matter. While the mathematical structure of matrix product states (MPS) is well understood through the MPS fundamental theorem, an analogous understanding for mixed-state tensor networks remains largely absent: if two purification tensors generate the same density matrix, how are they related? In this work, we initiate the study of a fundamental theorem for matrix product locally purifiable density operators (LPDOs) and focus on sequentially generated LPDOs (sLPDOs), a broad subclass admitting an interpretation in terms of successive applications of quantum channels on an initial state. We prove that, under suitable invertibility or cyclic conditions, two sLPDO representations generate the same density matrix for arbitrary system sizes if and only if they are related by a matrix product isometry acting on the purification bonds. Beyond the sLPDO setting, we provide a counterexample that suggests an obstruction to a general fundamental theorem for LPDOs with periodic boundary conditions. Finally, we discuss implications for mixed-state symmetry-protected topological phases, including the possibility of nontrivial phases protected only by weak symmetry conditions.

We construct an exactly solvable Hamiltonian lattice model realizing a 1+1d Dirac fermion, with exact microscopic vector and axial vector $U(1)$ symmetries. The mixed anomaly between these is accommodated by the not-on-site action of the symmetries. Our Hilbert space is a $Z_2$-graded tensor product of local $Z_2$-graded Hilbert spaces which include infinite dimensional rotor degrees of freedom. The Hamiltonian becomes manifestly exactly solvable after a locality-preserving unitary mapping to an equivalent fermionic Villain Hilbert space. Our construction also allows an exactly solvable realization of interacting fermionic Luttinger liquids. At the free Dirac fixed point, our Hamiltonian contains irrelevant interactions, which we compute to leading order.

Thermal fluctuations are generally expected to destroy order and restore symmetries at sufficiently high temperatures. Recently, however, a family of scalar theories in $2+1$ dimensions was shown to exhibit $\mathbb Z_2$ symmetry breaking that persists to arbitrarily high temperatures using a variety of approaches, including the $\epsilon$-expansion, the FRG, and large-$N$ techniques. Although the similarities among these theories suggest that they belong to the same universality class, this connection has not been established explicitly. In this work, we fill this gap. Using large-$N$ methods, we analytically study the biconical vector model in a range of spacetime dimensions, including $2+1$, at leading and next-to-leading order in the $1/N$ expansion. We determine the RG flow, fixed-point structure, and the CFT data of the infrared theory, reproducing and extending previous results and thereby unifying the apparently distinct constructions within a common analytic framework. We derive the effective potential, establish its stable minima at zero and finite temperature, and demonstrate spontaneous $\mathbb{Z}_2$ symmetry breaking at arbitrarily high temperatures for large finite $N$.

At large $N$, two coupled Sachdev-Ye-Kitaev models realize an eternal traversable wormhole with a discrete spectrum. We show that at finite $N$ the spectrum organizes into clusters labeled by operator size. Low-size clusters evolve into the conformal towers and define a weak-ergodicity-breaking subspace responsible for the long-lived wormhole revival dynamics. Moreover, the competition between size energy and size entropy provides a microscopic interpretation of the wormhole-black hole transition. These results reveal operator size as the bridge between the finite-$N$ spectrum and the emergent gravitational physics at large $N$.

In our recently published work (our Ref. 1) we revisited the gradient expansion approximation (GEA) of the interacting electron gas, and recalculated the leading-order contribution$-$with respect to the Wigner-Seitz radius $r_s$$-$to the coefficient $B_{xc}[n]$ of the square of the gradient of the electron density in the high-density and slowly varying limits. That work resolved historical controversies regarding these coefficients and demonstrated that serious misconceptions have led to incorrect constraints being imposed on popular functionals within the generalized gradient approximation (GGA). In the present paper, we extend this calculation to obtain the coefficient of the next-to-leading term, which scales as $r_s \ln(r_s)$ relative to the leading order. First, we establish a systematic framework to evaluate the integral expressions for the $b_{xc}$ coefficient of the leading term ($\sim q^2$) of the density-density response function in the long-wavelength limit ($q \to 0$)$-$a prerequisite for computing $B_{xc}[n]$. The significance of the calculation stems from the proof that the coefficient of this $r_s \ln(r_s)$ term receives no corrections from higher-order diagrammatic expressions. Consequently, our derived value serves as an exact, definitive constraint for future GGA functional development; in the high-density slowly-varying limit, any valid functional must reproduce the exact constraints established in both our previous work and the present paper.

Tensor-network methods have opened a powerful route for the study of dynamical spectral functions in two-dimensional quantum systems. However, existing approaches within the framework of infinite projected entangled-pair states construct the required renormalization tensors solely from the ground-state environment and can suffer from severe numerical instability. We identify the origin of this instability and introduce an excitation-tailored corner-transfer-matrix renormalization-group (ET-CTMRG) method to resolve it. By incorporating excitation tensors into the renormalization procedure, the method constructs a substantially more accurate effective Hamiltonian matrix and thereby yields reliable and well-converged excitation spectra. For Heisenberg antiferromagnets, it reduces truncation errors by orders of magnitude and for the particularly complex case of the supersolid phase in the triangular-lattice XXZ magnet $\mathrm{K_2Co(SeO_3)_2}$, it achieves excellent quantitative agreement with inelastic neutron-scattering measurements. ET-CTMRG therefore provides a robust framework for investigating the dynamical properties of strongly correlated quantum systems.

We report the synthesis of stoichiometric NiTe$_{2}$ single crystals via chemical vapor transport together with precise structural characterization. A combined analysis using powder and single crystal X-ray diffraction (XRD) was performed to determine lattice parameters and structural details. High-resolution single crystal XRD reveals no evidence of interstitial nickel, confirming a close-to-stoichiometric composition. This work establishes a reliable benchmark for the crystal structure of stoichiometric NiTe$_{2}$, offering a reference for future studies on its physical properties.

The time-dependent quantum geometric tensor, which captures dipole fluctuations of bound electrons, is essential for understanding the electronic properties of insulators, superconductors, and flat bands. It is often considered subleading for low-energy descriptions of metals that are dominated by intra-band processes. Here, we revisit this perspective and highlight scenarios where the quantum geometry of the wavefunctions close to the Fermi surface plays a significant role. We compute the time-dependent quantum geometric tensor for metals, explain its divergence, and contrast it against singular geometric tensors of Dirac and Weyl semi-metals. We identify the ratio of Drude to total spectral weight, $D/\mathcal{S}_1$, as a lattice-scale probe of bound versus itinerant charge, and quantify it in the kagome metal, where the two van Hove fillings respond differently despite identical Fermi surfaces.

The recent discovery of high-temperature superconductivity in pressurized bilayer La3Ni2O7 has sparked intense research interest, yet the microscopic mechanism governing its pressure-dependent superconducting transition temperature (Tc) remains elusive. In this work, we investigate the electronic and magnetic correlations of La3Ni2O7 under high pressure using a combination of density-functional theory (DFT), constrained random phase approximation (cRPA), and dynamical mean-field theory (DMFT). We find that while hydrostatic pressure enhances the interlayer hopping and the bare superexchange energy scale (4t2/U), it simultaneously drives the system toward a more itinerant regime by reducing the relative correlation strength (U/W). Crucially, our results reveal a distinct orbital-selective evolution: the Ni dx2-y2 states become increasingly itinerant, whereas the Ni dz2 orbitals retain a more localized character. This pressure-induced itinerancy significantly enhances the hybridization between the two, leading to a dramatic amplification of the Kondo-like screening of the local dz2 moments by the itinerant dx2-y2 electrons. Consequently, the effective magnetic exchange coupling (Jeff), which serves as the pairing glue, is suppressed in the high-pressure regime. Our findings suggest that the monotonic decrease of Tc at high pressures is driven by the dominance of Kondo screening over superexchange interactions, providing a coherent microscopic explanation for the dome-shaped superconducting phase diagram in La3Ni2O7.

We investigate the two-dimensional inhomogeneous Ising model (2DIM) on the kagom'e lattice by mapping it onto a particular non-symmetric eight-vertex model and constructing the corresponding $R$-matrix. Using a fermionic representation, we evaluate the partition function and derive explicit expressions for the main thermodynamic quantities. In the thermodynamic limit, we obtain an exact equation for the critical surface determining the phase transition of the model. We also calculate the free energy, specific heat, and spontaneous magnetization in the ferromagnetic case. Furthermore, we show that when one or two coupling constants vanish, the model reduces, respectively, to the square-lattice and one-dimensional Ising models. In both limits, our results reproduce the corresponding exact critical couplings and free energies.

We report a comprehensive muon spin relaxation ($\mu^+$SR) and bulk magnetization study of the antiferromagnetic (AFM) Weyl semimetal Mn$_3$Sn (composition Mn${2.99}$Sn). Mn$3$Sn is reported to exhibit a commensurate inverse triangular (IT) AFM phase, an incommensurate (IC) helical AFM phase, and a proposed low-temperature spin-glass-like state. In our sample, we identify the characteristic temperatures associated with these regimes as N'eel temperature ($T\mathrm{N} = 418$ K), a macroscopic bulk transition temperature between IT-AFM to IC helical phase ($T\mathrm{t} \approx 275$ K), and low-temperature transition $T_\mathrm{f} = 21$ K. Investigating the low-temperature regime below $T_\mathrm{f}$, we find no evidence of a static spin-glass state. Instead, the sample exhibits an increasing ferromagnetic (FM) component accompanied by a localized slowing of spin fluctuations, indicating that these phenomena may be decoupled. In the IC helical AFM phase, the zero-field (ZF) spectra are best described by damped oscillations with an empirical phase offset, consistent with anharmonic and amplitude-modulated order reported by scattering studies. Upon warming above 150 K, a continuous redistribution of muon spectral weight reveals a broad, homogeneous magnetic crossover between the IC helical and IT-AFM phases. In the commensurate IT-AFM phase above $T_\mathrm{t}$, a persistent missing fraction in the initial asymmetry indicates that a subset of implanted muons, corresponding to roughly 20% of the sample-related asymmetry, undergoes unresolved ultrafast depolarization. Finally, we observe temperature-driven shifts in muon site populations above 325 K. Ultimately, our results show a highly dynamic magnetic landscape in Mn$_3$Sn, demonstrating how its complex magnetic orders often coexist and evolve continuously with temperature.

Spin-ice materials are famous for their quasi-particle excitations that behave like magnetic monopoles. Magnetricity is the concept that these monopoles can conduct an AC magnetic current, in analogy with conduction electrons. While monopole dynamics has been intensively studied and is reasonably well understood, very little has been done to design devices in order to control magnetricity. Here we develop a theoretical proof of concept for the design of diodes and capacitors for the transport of monopoles. We use the property of systems with magnetic fragmentation, where spin-ice physics co-exists with long-range antiferromagnetic order. The key point is that magnetic order allows for the existence of domain walls. Under certain conditions of preparation, this domain wall is equivalent to an asymmetric filter for monopoles. In a given direction, positive charges can go through while negative ones are repelled; the opposite applies in the opposite direction. This asymmetry effectively functions like a diode for monopole current. Successive domain walls separate positive from negative charges with a vacuum of charge in between, producing a capacitor for monopoles. Once the capacitor is charged, it can in principle be used as a battery for monopoles. All microscopic mechanisms are explained and our proof of concept is validated by simulations of more than a million spins. Application to experiments are discussed for rare-earth pyrochlore oxides and artificial spin ice. Finally, we discuss in general terms how a domain wall in fragmented spin ice can also be seen as an emergent boundary separating two mirror "worlds" separated by time-reversal symmetry. Beyond spin ice, our work opens a promising direction of investigation for the dynamics of emergent quasi-particles crossing domain walls in chiral and nematic spin liquids, which also possess a broken symmetry.

Multiple-$Q$ magnetic orders combine continuous spin rotations with discrete crystalline sectors associated with translations and point-group transformations, producing a richer defect structure than conventional single-$Q$ magnets. We classify the bulk defects of all seven stable phases for $N=2$ and $3$ in the $M$-point triple-$Q$ Ginzburg–Landau theory with $(\Vfour\rtimes\Dthree)\times\OO(N)$ symmetry, where $\Vfour$ is the translation-generated Klein four-group. The atomic lattice is treated as a prescribed background, with lattice dislocations and disclinations excluded and the three Fourier fields retaining their physical $M$-point labels. The parent-group transformations continuously connected to the identity form $G_0=\{e\}\times\SO(N)$. For a reference-state stabilizer $H$, the connected component containing the reference state is $G_0/(H\cap G_0)$, not the quotient obtained by projecting $H$ onto spin space. This distinction gives the orthogonal triple-$Q$ phase the full manifold $\OO(3)$, with chirality walls and Abelian $\ZZ_2$ frame vortices rather than non-Abelian binary-polyhedral vortices. Every connected component of the $\OO(2)$ phases supports an integer $2\pi$ vortex, whereas fractional windings close only when attached to a discrete-domain wall and are linearly confined at nonzero wall tension. Translation symmetry further forbids cross-gradient bilinears, reducing the quadratic elastic sector to an isotropic and an $M$-point-locked anisotropic stiffness. The classification separates free internal defects, crystalline domain walls, and wall-bound composites in triple-$Q$ magnets.

We study the spin-partitioned entanglement Hamiltonian of the one-dimensional repulsive Hubbard model. By combining bosonization with exact diagonalization, we show that tracing out one spin species produces a modular Luttinger liquid, whose properties fundamentally differ from those of the physical system. While the modular spectrum is fully dispersionless and possesses a momentum-independent entanglement gap, its eigenstates exhibit algebraic correlations governed by a single effective Luttinger parameter equal to the geometric mean of the charge and spin Luttinger parameters. The resulting entanglement spectrum displays a universal branching hierarchy in excellent agreement with exact diagonalization. We further demonstrate that the modular ground state is nearly identical to that of the spinless Luttinger liquid. These results uncover a universal modular structure in interacting one-dimensional fermionic systems.