arXiv subjects

Tomohiro Soejima

Publications and source records attributed to Tomohiro Soejima.

At least 19 recordsLinked to original sources

arXiv2026

Non-uniform quantum geometry stabilizes generalized Wigner crystals

Moir\'e materials host fractional Chern insulators and electron crystals in close proximity, but the mechanism selecting between them remains an open question. We address this competition in Chern bands with ideal but momentum-dependent quantum geometry -- Aharonov-Casher bands. We present an ansatz wave function for generalized Wigner crystals and, by comparing its energy to that of the competing Laughlin-like state, map out the phase diagram at filling fraction $\nu=1/m$ as a function of the degree of geometric non-uniformity. Our work identifies quantum geometry-controlled zero point fluctuations of the charge density of the generalized Wigner crystal as the mechanism controlling its relative stability, implying a kind of quantum Lindemann criterion for the crystal-liquid phase boundary.

cond-mat.str-el↗

arXiv2026

Large scale neural quantum states reveal the interplay between superconductivity and quantum criticality in the Hofstadter-Hubbard model

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.

cond-mat.str-el↗

arXiv2026

Crystals Caught Doping: Metallic Wigner Crystals in Rhombohedral Graphene

Nearly a century after Wigner's initial proposal, electron crystals are now a topic of intense experimental and theoretical interest. However, most proposed crystalline phases are commensurate and therefore become insulating in the presence of even weak pinning. In this work we discuss when a commensurate Wigner crystal will spontaneously self dope and develop itinerant carriers, giving rise to an incommensurate and thus metallic Wigner crystal (MWC). We develop a general criterion for the instability of the commensurate crystal which involves the competition between the charge gap at commensurability and a ``packing bias'' whose sign selects whether electron or hole doping is preferred. We then apply these insights to rhombohedral multilayer graphene, where calculations for commensurate crystals reveal instabilities towards self-doping. Carrying out self-consistent Hartree-Fock over the landscape of incommensurate crystals reveals the phase diagram, where a broad MWC phase appears directly adjacent to an insulating Wigner crystal phase. Recent observations of an island of reversed Hall conductance near a putative Wigner crystal phase in rhombohedral graphene are naturally explained by our theory.

cond-mat.str-el↗

arXiv2025

Anyon Dispersion in Aharonov-Casher Bands and Implications for Twisted MoTe${}_2$

The discovery of fractional quantum anomalous Hall (FQAH) states in two-dimensional heterostructures has opened the door to realizing phases of dispersing anyons. Here, we develop an analytically controlled theory of anyon dispersion in FQAH states realized in ideal or Aharonov-Casher (AC) bands by projecting interactions onto the space of Laughlin quasiholes. Constructing quasihole momentum eigenstates allows efficient evaluation of the single quasihole dispersion using Monte Carlo. We find that the quasihole bandwidth grows with increasing quantum-geometry inhomogeneity of the AC band and with increasing interaction screening length. For realistic parameters relevant to the bands of twisted MoTe${}_2$, the quasihole bandwidth is of order 1 meV and increases with increasing displacement field, suggesting that itinerant-anyon physics may play an important role in sufficiently clean samples. Furthermore, we develop a microscopic Lagrangian framework in terms of a quasihole guiding-center coordinate, which reproduces the momentum-space formula for the dispersion. This approach reveals that quasihole dispersion originates from the combined effects of an interaction-generated periodic potential, arising from non-uniform quantum geometry of the single particle bands, and the quasihole many-body Berry phase arising from the background magnetic field. The latter endows the guiding-center coordinate with a noncommutative structure, converting the periodic potential into a finite dispersion. Finally, we outline how this framework generalizes to multiple quasiholes, enabling a microscopic theory of charged excitations in FQAH systems that retains only the anyon degrees of freedom.

cond-mat.str-el↗

arXiv2025

Rigorous lower bound on dynamical exponents in gapless frustration-free systems

This work rigorously establishes a universal lower bound $z\ge2$ for the dynamical exponent in frustration-free quantum many-body systems whose ground states exhibit power-law decaying correlations. The derivation relies on the Gosset-Huang inequality, providing a unified framework applicable across various lattice structures and spatial dimensions, independent of specific boundary conditions. Remarkably, our result can be applied to prove new bounds for dynamics of classical stochastic processes. Specifically, we utilize a well-established mapping from the time evolution of local Markov processes with detailed balance to that of frustration-free quantum Hamiltonians, known as Rokhsar-Kivelson Hamiltonians. This proves $z \ge 2$ for such Markov processes, which is an improvement over existing bounds. Beyond these applications, the quantum analysis of the $z\ge2$ bound is further broadened to include systems exhibiting hidden correlations, which may not be evident from purely local operators.

cond-mat.str-el↗

arXiv2025

Quantum Geometry Driven Crystallization: A Neural-Network Variational Monte Carlo Study

Wigner crystals are a paradigmatic form of interaction driven electronic order. A key open question is how Berry curvature and, more generally, quantum geometry reshape crystallization. The discovery of two-dimensional materials with relatively flat bands and pronounced Berry curvature has added fresh urgency to this question. Recent mean-field studies have proposed a topological variant of the Wigner crystal, the anomalous Hall crystal (AHC), with non-zero Chern number. However it remains unclear whether the AHC survives beyond the mean-field approximation. Here, we map out the ground-state phase diagram of the $λ$-jellium model - a simple model whose interaction strength and Berry curvature are independently tunable - using state-of-the-art neural-network variational Monte Carlo. The AHC is found to remain stable against quantum fluctuations. Surprisingly, quantum geometric effects are found to dramatically enhance crystallization. Both the AHC and the standard Wigner Crystal are stabilized at densities up to an order of magnitude above the critical density in the absence of quantum geometry, yet still significantly below the threshold predicted by mean-field theory. These striking results highlight the rich interplay between quantum fluctuations, quantum geometry, and crystallization, providing concrete guidance for experiments and enabling future explorations of fractionalized crystals and chiral superconductors.

cond-mat.str-el↗

arXiv2025

$λ$-Jellium Model for the Anomalous Hall Crystal

The jellium model is a paradigmatic problem in condensed matter physics, exhibiting a phase transition between metallic and Wigner crystal phases. However, its vanishing Berry curvature makes it ill-suited for studying recent experimental platforms that combine strong interactions with nontrivial quantum geometry. These experiments inspired the anomalous Hall crystal (AHC) -- a topological variant of the Wigner crystal. The AHC spontaneously breaks continuous translation symmetry but has a nonzero Chern number. In this work, we introduce $λ-$jellium, a minimal extension of the two-dimensional jellium model. Its Berry curvature distribution is controlled by a single parameter, $λ$, where $λ=0$ corresponds to the standard jellium model. This setup facilitates the systematic exploration of Berry curvature's impact on electron crystallization. The phase diagram of this model, established using self-consistent Hartree Fock calculations, reveals several interesting features: (i) The AHC phase occupies a large region of the phase diagram. (ii) Two distinct Wigner crystal phases, the latter enabled by quantum geometry, and two distinct Fermi liquid phases are present. (iii) A continuous phase transition separates the AHC and one of the WC phases. (iv) In some parts of the AHC phase, the lattice geometry is non-triangular, unlike in the classical Wigner crystal. In addition to elucidating the physics of correlated electrons with nonzero Berry curvature, we expect that the simplicity of the model makes it an excellent starting point for more advanced numerical methods.

cond-mat.str-el↗

arXiv2025

Phonons in Electron Crystals with Berry Curvature

Recent advances in 2D materials featuring nonzero Berry curvature have inspired extensions of the Wigner crystallization paradigm. This paper derives a low-energy effective theory for such quantum crystals, including the anomalous Hall crystal (AHC) with nonzero Chern number. First we show that the low frequency dispersion of phonons in AHC, despite the presence of Berry curvature, resembles that of the zero field (rather than finite magnetic field) Wigner crystal due to the commutation of translation generators. We explain how key parameters of the phonon theory such as elastic constants and effective mass can be extracted from microscopic models, and apply them to two families of models: the recently introduced $λ$-jellium model and a model of rhombohedral multilayer graphene (RMG). In the $λ$-jellium model, we explore the energy landscape as crystal geometry shifts, revealing that AHC can become `soft' under certain conditions. This causes transitions in lattice geometry, although the quantized Hall response remains unchanged. Surprisingly, the Berry curvature seems to enhance the effective mass, leading to a reduction in phonon speed. For the AHC in RMG, we obtain estimates of phonon speed and shear stiffness. We also identify a previously overlooked `kineo-elastic' term in the phonon effective action that is present in the symmetry setting of RMG, and leads to dramatic differences in phonon speeds in opposite directions. We numerically confirm these predictions of the effective actions by time-dependent Hartree-Fock calculations.

cond-mat.str-el↗

arXiv2025

Anyon Superconductivity from Topological Criticality in a Hofstadter-Hubbard Model

We argue that the combination of strong repulsive interactions and high magnetic fields can generate electron pairing and superconductivity. Inspired by the large lattice constants of moiré materials, which make large flux per unit cell accessible at laboratory fields, we study the triangular lattice Hofstadter-Hubbard model at one-quarter flux quantum per plaquette, where previous literature has argued that a chiral spin liquid separates a weak-coupling integer quantum Hall phase and a strong-coupling topologically-trivial antiferromagnetic insulator at a density of one electron per site. We argue that topological superconductivity emerges upon doping in the vicinity of the integer quantum Hall to chiral spin liquid transition. We employ exact diagonalization and density matrix renormalization group methods to examine this theoretical scenario and find that electronic pairing indeed occurs on both sides of criticality over a remarkably broad range of interaction strengths. On the chiral spin liquid side, our results provide a concrete model realization of the long-hypothesized mechanism of anyon superconductivity. Our study thus establishes a beyond-BCS mechanism for electron pairing in a well-controlled limit, relying crucially on the interplay between electron correlations and band topology.

cond-mat.str-el↗

arXiv2025

Robust superconductivity upon doping chiral spin liquid and Chern insulators in a Hubbard-Hofstadter model

Demonstrating superconductivity in purely repulsive Hubbard models is a compelling goal which underscores the counter-intuitive ability of Coulomb interactions to mediate superconductivity. Here, we present numerical evidence for robust superconductivity in a triangular Hubbard-Hofstadter model at $π/2$ flux per plaquette. Employing infinite density matrix renormalization group calculations on infinite cylinders of finite circumference, we observe superconducting ground states for a wide range of dopings, whose pair-correlations strengthen as the 2D limit is approached. At a density of one electron per site, Hubbard interactions have been reported to drive the insulating parent state of the superconductor from an integer quantum Hall (IQH) state to a chiral spin liquid (CSL). Our findings give credence to a recent proposal that proximity to the IQH-CSL transition serves to make chiral superconductivity energetically favorable on doping, and also correctly predicts the nature of the edge modes in the superconductor. On the CSL side, this suggests the superconductor can be thought of as arising from Laughlin's `anyon superconductivity' mechanism. Thus the Hubbard-Hofstadter model studied here offers a clean and experimentally accessible setup, potentially realizable in moiré heterostructures, for exploring the properties of anyonic matter at finite density and the interplay of topological order, quantum criticality and superconductivity.

cond-mat.str-el↗

arXiv2025

Anyon dispersion from non-uniform magnetic field on the sphere

The discovery of fractional quantum anomalous Hall states in moiré systems has raised the interesting possibility of realizing phases of itenerant anyons. Anyon dispersion is only possible in the absence of continuous magnetic translation symmetry (CMTS). Motivated by this, we consider anyons on the sphere in the presence of a non-uniform magnetic field which breaks the ${\rm SU}(2)$ rotation symmetry, the analog of CMTS on the sphere, down to a ${\rm U}(1)$. This allows us to study the energy dispersion of the anyons as a function of $L_z$ angular-momentum, while maintaining the perfect flatness of single-particle dispersion. We parametrize the non-uniform field by a real parameter $R$ which concentrates the field at the north (south) pole for $R>1$ ($R < 1$), and show that, for our choice of field, any $p$-body correlation function evaluated in the space of Laughlin quasiholes can be mapped \emph{exactly} to a corresponding $p$-body correlation function in uniform field. In the thermodynamic limit, this enables us to analytically compute the interaction-generated spatially varying potential felt by the anyons. Remarkably, such spatially varying potential is sufficient to generate dispersion for the anyons, which we compute exactly, up to an overall scaling constant. The anyon dispersion in our model describes azimuthal motion around the sphere at a constant height, similar to spin precession. Our work therefore serves as a concrete demonstration that interaction alone can generate nonzero anyon dispersion in the presence of inhomogeneous magnetic field.

cond-mat.str-el↗

arXiv2025

Topological constraint on crystalline current

How much current does a sliding electron crystal carry? The answer to this simple question has important implications for the dynamic properties of the crystal, such as the frequency of its cyclotron motion, and its phonon spectrum. In this work we introduce a precise definition of a sliding crystal and compute the corresponding current $\mathbf{j}_c$ for topological electron crystals in the presence of magnetic field. Our result is fully non-perturbative, does not rely on Galilean invariance, and applies equally to Wigner crystals and (anomalous) Hall crystals. In terms of the electron density $\rho$ and magnetic flux density $\phi$, we find that $\mathbf{j}_c = e(\rho-C\phi)\mathbf{v}$. Surprisingly, the current receives a contribution from the many-body Chern number $C$ of the crystal. When $\rho = C\phi$, sliding crystals therefore carry zero current. The crystalline current fixes the Lorentz force felt by the sliding crystal and the dispersion of low-energy phonons of such crystals. This gives us a simple counting rule for the number of gapless phonons: if a sliding crystal carries nonzero current in a magnetic field, there is a single gapless mode, while otherwise there are two gapless modes. This result can also be understood from anomaly-matching of emanant discrete translation symmetries -- an idea that is also applicable to the dispersion of skyrmion crystals. Our results lead to novel experimental implications and invite further conceptual developments for electron crystals.

cond-mat.str-el↗

arXiv2025

Higher Hall conductivity from a single wave function: Obstructions to symmetry-preserving gapped edge of (2+1)D topological order

A (2+1)D topological ordered phase with U(1) symmetry may or may not have a symmetric gapped edge state, even if both thermal and electric Hall conductivity are vanishing. It is recently discovered that there are "higher" versions of Hall conductivity valid for fermionic fractional quantum Hall (FQH) states, which obstructs symmetry-preserving gapped edge state beyond thermal and electric Hall conductivity. In this paper, we show that one can extract higher Hall conductivity from a single wave function of an FQH state, by evaluating the expectation value of the "partial rotation" unitary which is a combination of partial spatial rotation and a U(1) phase rotation. This result is verified numerically with the fermionic Laughlin state with $ν=1/3$, $1/5$, as well as the non-Abelian Moore-Read state. Together with topological entanglement entropy, we prove that the expectation values of the partial rotation completely determines if a bosonic/fermionic Abelian topological order with U(1) symmetry has a symmetry-preserving gappable edge state or not. We also show that thermal and electric Hall conductivity of Abelian topological order can be extracted by partial rotations. Even in non-Abelian FQH states, partial rotation provides the Lieb-Schultz-Mattis type theorem constraining the low-energy spectrum of the bulk-boundary system. The generalization of higher Hall conductivity to the case with Lie group symmetry is also presented.

cond-mat.str-el↗

arXiv2025

Rigorous lower bound of the dynamical critical exponent of the Ising model

We study the kinetic Ising model under Glauber dynamics and establish an upper bound on the spectral gap for finite systems. This bound implies the critical exponent inequality $z \geq 2$, thereby rigorously improving the previously known estimate $z \geq 2 - η$. Our proof relies on the mapping from stochastic processes to frustration-free quantum systems and leverages the Simon--Lieb and Gosset--Huang inequalities.

cond-mat.stat-mech↗

arXiv2025

Characterization of randomness in quantum circuits of continuous gate sets

In the accompanying paper of arXiv:2408.13472, we have established the method of characterizing the maximal order of asymptotic unitary designs generated by symmetric local random circuits, and have explicitly specified the order in the cases of $\mathbb{Z}_2$, U(1), and SU(2) symmetries. Here, we provide full details on the derivation of the main theorems for general symmetry and for concrete symmetries. Furthermore, we consider a general framework where we have access to a finite set of connected compact unitary subgroups, which includes symmetric local unitary gate sets.

quant-ph↗

arXiv2025

Unitary Designs of Symmetric Local Random Circuits

We have established the method of characterizing the unitary design generated by a symmetric local random circuit. Concretely, we have shown that the necessary and sufficient condition for the circuit asymptotically forming a t-design is given by simple integer optimization for general symmetry and locality. By using the result, we explicitly give the maximal order of unitary design under the $\mathbb{Z}_2$, U(1), and SU(2) symmetries for general locality. This work reveals the relation between the fundamental notions of symmetry and locality in terms of randomness.

quant-ph↗

arXiv2024

Quadratic dispersion relations in gapless frustration-free systems

Recent case-by-case studies revealed that the dispersion of low energy excitations in gapless frustration-free Hamiltonians is often quadratic or softer. In this work, we argue that this is actually a general property of such systems. By combining a previous study by Bravyi and Gosset and the min-max principle, we prove this hypothesis for models with local Hilbert spaces of dimension two that contains only nearest-neighbor interactions on cubic lattice. This may be understood as a no-go theorem realizing gapless phases with linearly dispersive excitations in frustration-free Hamiltonians. We also provide examples of frustration-free Hamiltonians in which the plane-wave state of a single spin flip does not constitute low energy excitations.

cond-mat.str-el↗

arXiv2024

Tensor Network Python (TeNPy) version 1

TeNPy (short for 'Tensor Network Python') is a python library for the simulation of strongly correlated quantum systems with tensor networks. The philosophy of this library is to achieve a balance of readability and usability for new-comers, while at the same time providing powerful algorithms for experts. The focus is on MPS algorithms for 1D and 2D lattices, such as DMRG ground state search, as well as dynamics using TEBD, TDVP, or MPO evolution. This article is a companion to the recent version 1.0 release of TeNPy and gives a brief overview of the package.

cond-mat.str-el↗