arXiv subjects

Haruki Watanabe

Publications and source records attributed to Haruki Watanabe.

At least 19 recordsLinked to original sources

arXiv2026

Absence of nontrivial local conserved quantities in a class of $U(1)$-symmetric spin-1 chains

We prove the absence of nontrivial local conserved quantities in a class of $U(1)$-symmetric spin-$1$ chains with nearest-neighbor interactions in which some of the quadrupolar couplings vanish, a class that is not covered by previous studies. Applying the technique of Shiraishi to these systems, we show that, for every model in this class on a periodic chain of $N$ sites, there is no $k$-local conserved quantity for any $3\le k\le N/2$. In particular, for a frustration-free spin-$1$ chain that exhibits spontaneous $U(1)$ symmetry breaking at zero temperature in one spatial dimension, we prove that every local conserved quantity with support up to half of the system size is a linear combination of the identity, the total magnetization $S^z$, and the Hamiltonian itself. This rigorously establishes that, unlike the Heisenberg ferromagnet, the model admits no local order parameter commuting with the Hamiltonian, so that its continuous symmetry breaking is enabled by the frustration-free structure rather than by a conserved order parameter. We also prove the absence of $k$-local conserved quantities for $3\le k\le N/2$ in the periodic Motzkin chain, a frustration-free spin-$1$ chain closely related to the original Motzkin chain, for which spontaneous $U(1)$ symmetry breaking at zero temperature has also been reported.

cond-mat.str-el↗

arXiv2026

Quantized topological invariant of symmetry-projected Gibbs states

We study Gibbs states projected onto the symmetric sector of contractible one-form symmetries. In a three-dimensional cluster-model interpolation, this projection stabilizes symmetry-protected topological and projected-paramagnetic phases, both sharply distinct from thermal disorder. A flux-twisted membrane invariant distinguishes these three phases by the values $-1,+1,0$, respectively. These values are exact on the endpoint, self-dual, zero-temperature, and infinite-temperature lines; elsewhere their quantization requires positive spatial-sheet, winding-line, and interface tensions. Quantum Monte Carlo supports the quantization through tension diagnostics and direct finite-size estimates.

cond-mat.str-el↗

arXiv2026

Distinct finite-temperature phase diagrams of non-invertible Kennedy--Tasaki duals

Do two Hamiltonians related by a non-invertible transformation necessarily share the same finite-temperature phase diagram? For a cluster-model interpolation $H(s)$ and its Kennedy--Tasaki dual $\tilde H(s)$, the map is a partial isometry and equates only their all-plus-sector partition functions. In one dimension, thermal order is forbidden on both sides, leaving only the common zero-temperature transition at $s=\tfrac12$. In three dimensions, however, the inequivalence is exact already at $s=0$: the cluster model has an analytic paramagnetic free energy, whereas its dual $\mathbb Z_2$ gauge theory has a deconfinement transition at $T_c\approx1.31$. Quantum Monte Carlo shows that the mismatch occupies a finite window of the interpolation, marked by a self-dual frozen wedge on the cluster side and a deconfined dome on the gauge side; once both close the two phase diagrams agree again, coinciding over the entire remaining interval up to the shared trivial endpoint $s=1$.

cond-mat.str-el↗

arXiv2026

Phase distinction of Gibbs states without symmetry breaking: topological invariants of the 3D toric code

We study the finite-temperature topological order of the three-dimensional $\mathbb{Z}_2$ toric code in a generic magnetic field, where every higher-form symmetry is explicitly broken and can at most be emergent. We show perturbatively, and confirm by large-scale quantum Monte Carlo at fields up to half the zero-temperature critical values, that the topological entanglement entropy stays quantized at $\gamma = \ln 2$ throughout the topological phase -- at finite temperature and under the symmetry-breaking field alike -- and collapses to $0$ across the thermal transition, a quantization protected geometrically by the Bianchi identity rather than by any exact symmetry of the system. The plateau $\gamma = \ln 2$ is, however, not invariant under quasi-local channels: a constant-depth channel can generate this identical quantized value from a trivial product state. We therefore introduce the decoded Wilson-loop correlation $f_W$ -- the connected correlator of Wilson loops read out after error correction -- which quantizes to $1$ in the topological phase and $0$ in the trivial phase as $L\to\infty$. Unlike $\gamma$, $f_W$ is a quasi-local-channel invariant: it is pinned to $0$ on every quasi-local-channel image of a product state and to $1$ in the topological phase, so no quasi-local channel carries the trivial phase to the topological one, and a fortiori no two-way equivalence connects them -- a robust topological invariant of the mixed state.

cond-mat.str-el↗

arXiv2026

Monte Carlo Study of the Phase Transition of the $XY$ Model on a Diamond Lattice

We study the phase transition of the classical $XY$ model on a diamond lattice by Monte Carlo simulations using the Wolff cluster algorithm. Finite-size scaling (FSS) analysis of the Binder cumulant and the second-moment correlation length ratio $\xi_{2\rm nd}/L$ yields $T_c = 1.30036(1)$ and $\nu = 0.671(6)$. Data collapse of both quantities confirms the three-dimensional $XY$ universality class.

cond-mat.str-el↗

arXiv2026

Topological Phase Transitions and Their Thermodynamic Fate in Arbitrary-$S$ Pyrochlore Spin Ice

We develop a self-contained theoretical framework that classifies the topological phases and critical phenomena of classical pyrochlore magnets with arbitrary spin $S$, subject to competing exchange and single-ion anisotropies. In the small-$w$ regime, where the single-ion term favors low spin amplitudes, exact dualities reveal a dichotomy: integer spins exhibit a continuous 3D $XY$ deconfinement transition, whereas half-integer spins remain in a $U(1)$ Coulomb liquid without any transition. In the large-$w$ regime, where the local spin amplitudes are maximized ($|S^z| = S$), the macroscopic flux is quantized to multiples of $2S$. By mapping the defect structure to topological loop gases, we prove that the compatibility between the physical ice rule and the emergent $\mathbb{Z}_{2S}$ flux conservation holds if and only if $S \le 3/2$. For $S=3/2$, this maps the system to the 3-state Potts model, whose symmetry-allowed cubic invariant drives a first-order transition. For $S \ge 2$, monopole contamination breaks the discrete clock mapping. Using an exact decomposition of the partition function, we show that the hierarchical string fusion cascade exponentially suppresses the discrete perturbations, which act as a dangerously irrelevant operator at the 3D $XY$ fixed point, protecting 3D $XY$ criticality. Finally, incorporating thermal monopoles, we show that they act as a symmetry-breaking effective magnetic field that severs defect strings. Consequently, the continuous transitions are rounded into crossovers, whereas the first-order $S=3/2$ transition is predicted to survive at finite temperatures, terminating at a critical endpoint. Classical Monte Carlo simulations for $S$ up to $7/2$ corroborate these analytical predictions.

cond-mat.str-el↗

arXiv2026

Continuous crossover between high-pressure ice phases VII and X driven by monopole screening: a model study

The proton-disordered molecular phase of water ice (ice-VII) and its ultrahigh-pressure non-molecular phase (ice-X) share identical macroscopic crystal symmetry (space group $Pn\bar{3}m$). This raises a fundamental thermodynamic question: are they distinct phases separated by a singularity, or are they adiabatically connected via a continuous crossover? To resolve this paradox, we investigate the finite-temperature phase diagram of high-pressure ices VII and X, as well as VIII, the proton-ordered phase that emerges at lower temperatures, using an effective classical spin-$1$ Blume-Capel model on the pyrochlore lattice. Through Monte Carlo simulations, we demonstrate that within this model, the transformation between the states corresponding to ice-VII and ice-X lacks a thermodynamic singularity, as characterized by non-divergent and non-coinciding peaks in the specific heat and susceptibility associated with the $S^z=0$ occupation. We attribute this continuous crossover behavior to the topological fragility of the hydrogen-bond network: the thermal proliferation of point-like monopole excitations (violations of the ice rules) induces Debye-H\"{u}ckel screening of the emergent gauge field, destroying the topological Coulomb phase at any finite temperature. In contrast, the destruction of the proton-ordered ice-VIII phase involves spontaneous symmetry breaking and remains a first-order phase transition. Our findings provide a microscopic rationale that reconciles the macroscopic crystallographic symmetries of dense ice with its underlying topological properties.

cond-mat.str-el↗

arXiv2026

Dualities and Topological Classification of the $S=1$ Pyrochlore Spin Ice

We resolve the phase diagram of the $S=1$ pyrochlore spin ice, which exhibits trivial paramagnetic, U(1) Coulomb, and spin nematic phases. In the monopole-free limit, the system can be effectively mapped onto 3D $XY$ and Ising loop-gas models depending on the spin anisotropy, which provides theoretical estimates for the phase boundaries, while a macroscopic flux vector classifies the topological sectors via geometric parity rules. At finite temperatures, thermal monopoles act as a symmetry-breaking field in both 3D $XY$ and Ising loop-gas pictures, rounding the phase transitions into continuous crossovers. These theoretical findings are corroborated by classical Monte Carlo simulations.

cond-mat.str-el↗

arXiv2025

Third-harmonic generation in superconductors: Role of quantum geometry in the competition between Higgs mode and quasiparticles

Collective modes in superconductors, such as the Higgs mode, offer deep insights into the nature of condensates. Third-harmonic generation (THG) is a primary tool for probing the Higgs mode, but its signal competes with that of quasiparticle excitations depending on impurity scattering rates. In particular, in the clean regime the standard BCS theory generally predicts the dominance of quasiparticle contributions. Here, we propose and demonstrate that the quantum geometry of electronic bands can be a key mechanism governing this competition. By developing a formalism that explicitly incorporates the quantum metric, and applying it to a tunable model of a dispersive-band superconductor, we show that the quantum metric can dramatically amplify the nonlinear light-Higgs coupling by several orders of magnitude. Our results establish that a large quantum metric can cause the Higgs mode to dominate the THG response, resolving the puzzle of Higgs and quasiparticle competition in the clean regime and identifying band geometry as a crucial ingredient for designing and understanding the nonlinear response of superconductors.

cond-mat.supr-con↗

arXiv2025

Projective Representations, Bogomolov Multiplier, and Their Applications in Physics

We present a pedagogical review of projective representations of finite groups and their physical applications in quantum many-body systems. Some of our physical results are new. We begin with a self-contained introduction to projective representations, highlighting the role of group cohomology, representation theory, and classification of irreducible projective representations. We then focus on a special subset of cohomology classes, known as the Bogomolov multiplier, which consists of cocycles that are symmetric on commuting pairs but remain nontrivial in group cohomology. Such cocycles have important physical implications: they characterize (1+1)D SPT phases that cannot be detected by string order parameters and give rise, upon gauging, to distinct gapped phases with completely broken non-invertible $\mathrm{Rep}(G)$ symmetry. We construct explicit lattice models for these phases and demonstrate how they are distinguished by the fusion rules of local order parameters. We show that a pair of completely broken $\mathrm{Rep}(G)$ SSB phases host nontrivial interface modes at their domain walls. As an example, we construct a lattice model where the ground state degeneracy on a ring increases from 32 without interfaces to 56 with interfaces.

cond-mat.str-el↗

arXiv2025

Quasi-local Frustration-Free Free Fermions

Recent studies have revealed that frustration-free models, expressed as sums of finite-range interactions or hoppings, exhibit several properties markedly different from those of frustrated models. In this work, we demonstrate that, by relaxing the finite-range condition to allow for exponentially decaying hoppings, one can build gapped frustration-free systems that realize Chern insulators as well as quasi-degenerate ground states with finite-size splittings. Moreover, by permitting power-law decaying hoppings, we also construct a gapless band metal whose finite-size gap scales inversely with the system size $L$. These findings serve as an important step toward clarifying the general properties of frustration-free systems and those represented by tensor network states.

cond-mat.str-el↗

arXiv2025

$\mathbb{Z}_N$ generalizations of three-dimensional stabilizer codes

In this work, we generalize several three-dimensional Z2 stabilizer models--including the X-cube model, the three-dimensional toric code, and Haah's code--to their ZN counterparts. Under periodic boundary conditions, we analyze their ground state degeneracies and topological excitations, and uncover behaviors that strongly depend on system size. For the X-cube model, we identify excitations with mobility restricted under local operations but relaxed under nonlocal ones derived from global topology. These excitations, previously confined to open boundaries in the Z2 model, now appear even under periodic boundaries. In the toric code, we observe nontrivial braiding between string and point excitations despite the absence of ground state degeneracy, indicating long-range entanglement independent of topological degeneracy. Again, this effect extends from open to periodic boundaries in the generalized models. For Haah's code, we find new excitations--fracton tripoles and monopoles--that remain globally constrained, along with a relaxation of immobility giving rise to lineons and planons. These results reveal new forms of topological order and suggest a broader framework for understanding fracton phases beyond the conventional Z2 setting.

cond-mat.str-el↗

arXiv2025

Frustration-free free fermions

We develop a general theory of frustration-free free-fermion systems and derive the necessary and sufficient conditions for such Hamiltonians. Assuming locality and translation invariance, we find that any band touching between the valence and the conduction bands is always quadratic or softer, which rules out the possibility of describing Dirac and Weyl semimetals using frustration-free local Hamiltonians. We further construct a frustration-free free-fermion model on the honeycomb lattice and show that its density fluctuations acquire an anomalous gap originating from the diverging quantum metric associated with the quadratic band-touching points. Nevertheless, an $O(1/L^2)$ finite-size scaling of the charge-neutral excitation gap can be verified even in the presence of interactions, consistent with the more general results we derive in an accompanying work [arXiv:2503.12879].

cond-mat.str-el↗

arXiv2025

Frustration-free free fermions and beyond

Frustration-free Hamiltonians provide pivotal models for understanding quantum many-body systems. In this paper, we establish a general framework for frustration-free fermionic systems. First, we derive a necessary and sufficient condition for a free fermion model to be frustration-free. In the case of translation-invariant, noninteracting systems, we show that any band touching between the valence and conduction bands is at least quadratic. Furthermore, by extending the Gosset-Huang inequality to fermionic systems, we demonstrate that even in interacting and non-translation-invariant cases, the finite-size gap of gapless excitations scales as $O((\log L)^2/L^2)$, provided the ground-state correlation function exhibits a power-law decay. Our results provide a foundation for studying frustration-free fermionic systems, including flat-band ferromagnetism and $\eta$-pairing states.

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 $z \geq 2 - \eta$. 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

Gauge-invariant electromagnetic responses in superconductors

Gauge invariance is essential for making physically meaningful predictions. In superconductors, mean-field Hamiltonians that explicitly break $U(1)$ symmetry often yield gauge-dependent results. While this issue has been resolved for linear responses in conventional superconductors, a unified framework that also covers unconventional superconductors and nonlinear responses has yet to be established. In this study, we present a comprehensive theoretical framework that enables gauge-invariant calculations of electromagnetic responses at arbitrary orders in external fields, applicable to both conventional and unconventional superconductors. Our construction generalizes the consistent-fluctuation-of-the-order-parameter (CFOP) approach to full photon vertices and admits a diagrammatic representation of the response kernel in terms of Feynman diagrams.

cond-mat.supr-con↗

arXiv2024

A gauge-invariant formulation of optical responses in superconductors

Superconductors are often discussed in the mean-field approximation that breaks $U(1)$ symmetry. Since the $U(1)$ symmetry underlies the charge conservation, naive application of response theory sometimes gives results that are not gauge-invariant. We study the effect of vertex corrections on the electromagnetic responses of superconductors by employing the gauge-invariant formulation, called consistent fluctuations of order parameters, that manifestly satisfy the Ward identity. For inversion broken two-band superconductors, we find that the linear and second-order optical responses are significantly affected by vertex corrections and the conductivities near the gap energy almost completely disappear. We also investigate the linear optical responses in $d$-wave superconductors and obtained qualitatively different results compared to the result using the solution to the Bethe-Salpeter equation. The full photon vertex used in our study, manifestly satisfies the Ward identity. Our results demonstrate the fundamental importance of vertex corrections in exploring optical responses in superconductors.

cond-mat.supr-con↗

arXiv2024

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↗