arXiv subjects

Hyun-Yong Lee

Publications and source records attributed to Hyun-Yong Lee.

At least 19 recordsLinked to original sources

arXiv2026

Magnetic-texture winding controls fermion-parity switches in an interacting $p$-wave magnet ring

Coplanar magnetic spirals map locally onto uniform spin--orbit-coupled wires, but on a ring the rotating spin frame can change the electronic boundary condition. We prove, level by level in every fixed-particle-number sector, that even and odd texture windings impose boundary phases separated by half the single-electron flux period. Changing the winding by one also changes the physical pitch in inverse proportion to the circumference; a symmetric comparison removes this leading pitch correction. In the number-conserving topological phase, a global parity constraint then reverses the fermion-parity assignment of neighboring phase-winding branches. Density-matrix renormalization-group simulations show this reversal, support an Ising transition coexisting with a gapless charge mode, and relate the finite-size parity splitting to an independently calculated charge stiffness. Magnetic-texture winding thus changes the many-body spectrum through a global boundary condition that is not determined by the local band dispersion, providing a closed-geometry, number-conserving probe of topological pairing.

cond-mat.str-el↗

arXiv2026

Universal Information-Theoretic Structure of the Quasi-Stationary Domany--Kinzel Automaton

We characterize the quasi-stationary distribution (QSD) of the bond directed-percolation line of the Domany--Kinzel automaton using a matrix-product-state representation of the probability distribution, obtained by projecting out the absorbing state and iterating the transfer matrix. Unlike moment- or sampling-based methods, this yields the full conditional distribution and direct access to information-theoretic diagnostics. The spatial structure of the QSD changes sharply across the transition: the active phase is bulk-like with finite density, whereas in the inactive phase the surviving activity collapses into a single flock -- the smallest interval containing all active sites -- occupying a vanishing fraction of the chain. Throughout the inactive phase the bipartite mutual information of the QSD equals the entropy of a single binary choice -- whether the flock lies to the left or right of the cut -- so the surviving clusters together encode just one bit of positional information, corresponding to a single effective cluster.

cond-mat.stat-mech↗

arXiv2026

Data-efficient reconstruction of critical quantum dynamics via blind fractional-envelope extrapolation

Simulating real-time dynamics of quantum systems is often limited to short times by entanglement growth. Finite-pole reconstructions such as linear prediction and related machineries extrapolate such data reliably when the spectrum is a finite set of excitations, but at criticality the low-energy spectrum is a power-law continuum $A(ω)\sim|ω|^{α-1}$ -- a branch cut whose real-time tail $G(t)\sim t^{-α}$ finitely many poles cannot represent. Here we develop a fractional-calculus-motivated envelope extrapolation for such data. Its structure is motivated by a fractional form of Schwinger--Dyson (fSD) equation, in which the Laplace symbol $s^α$ carries the branch cut analytically while the residual self-energy remains meromorphic. On real data we employ the corresponding operational alternative -- the exponent $α$ is selected blindly inside the fit window, the signal is detrended by $t^α$, the residual is fitted by a stabilized finite-pole model, and the algebraic envelope is restored. On the critical XXZ chain this blind fractional-envelope method (fSD for short) extrapolates short-time data typically several-fold more accurately than finite-pole methods, with the exponent $α$ identified blindly from the fit window alone and bracketing the closed-form Luttinger value at weak coupling. The same blind search finds the $z=2$ dilute-magnon exponent $α=1/2$ at the $Δ=1$ saturation transition, and the advantage persists in the gapped free-magnon phase with its sharp band edges. On noncritical dynamical mean-field spectra, whose low-frequency response is regular, fSD by contrast fails to select any stable fractional envelope and reduces to the standard pole result rather than manufacturing a spurious power law, making it an efficient and accurate route to quantum critical dynamics when only short simulation times are accessible.

cond-mat.str-el↗

arXiv2026

Topological phase transition of deformed ${\mathbb Z}_3$ toric code

We investigate topological phase transitions in a family of deformed $\mathbb Z_3$ toric-code wavefunctions prepared from a cluster state by local deformations and projective measurements. Their norms map to the $Q=3$ Potts model for single-parameter deformations and to a three-state Ashkin--Teller-like (AT$_3$) construction with two independent four-spin couplings in the general case. Projected entangled-pair-state (PEPS) and variational uniform matrix-product-state (VUMPS) calculations identify the toric-code (TC) phase and phases in which electric ($e$) anyons are confined or condensed. These phases are separated by critical structures with central charges $c=4/5$, $8/5$, and isolated $c=1$ antiferromagnetic (AFM) endpoints. A normalized finite-distance $e$-anyon pair-state norm provides a Fredenhagen--Marcu-type check of the confinement boundary, while the topological data of the quantum double $D(\mathbb Z_3)$ imply a topological entanglement entropy $γ=\log3$ throughout the gapped toric-code phase. Relative to the $\mathbb Z_2$ case, the absence of sign-change folding leaves the AFM endpoints unfolded, and the extreme deformation reaches square ice with an emergent $U(1)$ one-form symmetry, Hilbert-space fragmentation, and exact scar configurations.

quant-ph↗

arXiv2026

Spin-orbit-induced quantum chiral phases

The scalar spin chirality (SSC), whose nonzero value $\langle {\bf S}_i \cdot ({\bf S}_j \times {\bf S}_k) \rangle \neq 0$ implies the breaking of time-reversal and certain point-group symmetries in the ground state, is a key quantity characterizing chiral magnetism in both classical and quantum settings. The classical SSC is manifested, for instance, in skyrmion crystal phase, while the quantum SSC is still highly sought after in various frustrated spin-1/2 models. An interesting possibility that has not been explored so far is the case in which SSC is symmetry-wise allowed, yet remains zero classically due to the collinear or coplanar arrangement of spins, but is generated by virtue of quantum fluctuation. We demonstrate the existence of precisely such a phase in a spin-1/2 triangular-lattice model with XXZ interaction, spin-orbit-induced exchange interactions, and an external magnetic field. Using iDMRG, we thoroughly map out the phase diagram of the model and identify several phases with coexisting magnetic order and SSC. The nonzero SSC arises despite the classical magnetic order being collinear or coplanar. We provide detailed magnon analysis to ascribe its origin to quantum fluctuations around classical magnetic order. The estimate of SSC from magnon analysis agrees with iDMRG results quantitatively. We map out the magnon spectrum and its Berry curvature, culminating in the prediction of finite thermal Hall conductivity in these phases with SSC.

cond-mat.str-el↗

arXiv2026

Projector, Neural, and Tensor-Network Representations of $\mathbb{Z}_N$ Cluster and Dipolar-cluster SPT States

The $\mathbb{Z}_N$ cluster-state wavefunction, a paradigmatic example of symmetry-protected topological (SPT) order with $\mathbb{Z}_N \times \mathbb{Z}_N$ symmetry, is expressed in various equivalent ways. We identify the projector-based scheme called the $P$-representation as the efficient way to express cluster and dipolar cluster state's wavefunctions. Employing the restricted Boltzmann machine scheme to re-write the interaction matrix in the $P$-representation in terms of neural weight matrices allows us to develop the neural quantum state (NQS) and the matrix product state (MPS) representations of the same state. The NQS and MPS representations differ only in the way the weight matrices are split and grouped together in a matrix product. For both $\mathbb{Z}_N$ cluster and dipolar cluster states, we derive in closed form the weight function $W(s,h)$ that couples physical spins $s$ to hidden variables $h$, generalizing the previous construction for $Z_2$ cluster states to $\mathbb{Z}_N$. For the dipolar cluster state protected by two charge and two dipole symmetries, the procedure we have developed leads to the tensor product state (TPS) representation of the wavefunction where each local tensor carries three virtual indices connecting a given site to two nearest neighbors and one further neighbor. We benchmark the resulting TPS construction against conventional MPS representation using density-matrix renormalization group simulations and argue that the TPS could offer a more efficient representation for some modulated SPT states. As a by-product of the investigation, we generalize the previous $Z_2$ matrix product operator construction of the Kramers-Wannier (KW) operator to $\mathbb{Z}_N$ and interprets it as the dipolar generalization of the discrete Fourier transform on $\mathbb{Z}_N$ variables. The new interpretation naturally explains why the KW map is non-invertible.

cond-mat.dis-nn↗

arXiv2026

Spin-orbit-induced Instability and Finite-Temperature Stabilization of a Triangular-lattice Supersolid

Geometrically frustrated triangular-lattice magnets provide fertile ground for realizing intriguing quantum phases such as spin supersolids. A common expectation is that spin-orbit coupling (SOC), which breaks continuous spin rotational symmetry, destabilizes these phases by gapping their low-energy modes. Revisiting this assumption, we map out the SOC-field phase diagram of a frustrated triangular-lattice magnet using spin-wave theory and infinite density-matrix renormalization group (iDMRG) simulations. We find that while infinitesimally weak SOC indeed drives a zero-temperature instability of the supersolid by opening a gap, certain supersolid states remain thermodynamically stable at non-zero temperatures. This reveals a previously unrecognized mechanism in which thermal fluctuations counteract SOC to stabilize supersolidity. The resulting finite-temperature supersolids retain key responses, including a giant magnetocaloric effect, highlighting their potential relevance to real materials. At larger SOC, the system transitions into distinct magnetic orders, including a skyrmion lattice, completing a unified phase diagram.

cond-mat.str-el↗

arXiv2025

Dynamics of one-dimensional spin models via complex-time evolution of tensor networks

Studying the real-time dynamics of strongly correlated systems poses significant challenges, which have recently become more manageable thanks to advances in density matrix renormalization group (DMRG) and tensor network methods. A notable development in this area is the introduction of a complex-time evolution scheme for tensor network states, originally suggested for solving Anderson impurity model and designed to suppress the growth of entanglement under time evolution. In this study, we employ the complex-time evolution scheme to investigate the dynamics of one-dimensional spin systems, specifically the transverse-field Ising model (TFIM) and the XXZ model. Our analysis revisits the dynamic critical exponent $z$ of the TFIM and explores the dynamical structure factor in both gapped and gapless states of the XXZ model. Importantly, the complex-time evolution reproduces the results of real-time evolution while mitigating the rapid growth of quantum entanglement typically associated with the latter. These results demonstrate that the combination of complex-time evolution and extrapolation provides a robust and efficient framework for studying the dynamics of complex quantum systems, enabling more comprehensive insights into their behavior.

cond-mat.str-el↗

arXiv2025

Nested Shadows of Anyons:A Framework for Identifying Topological Phases

The 1-form symmetries in two-dimensional topological systems are ``shadowed'' as global symmetries in their one-dimensional quantum transfer matrices. In this work, we introduce a distinct shadow effect arising from the pair-creation of anyons, which manifests as a local symmetry of the quantum transfer matrix. The interplay between these two shadow effects provides a powerful framework for characterizing topological phases without extensive numerical simulations. Specifically, we derive the phase diagram of the filtered toric code state and precisely identify phase boundaries using the nested shadows of anyons. Additionally, we reveal that a class of topological states host gapless edge modes protected by 1-form symmetry rather than global symmetry. Finally, we apply our approach to the three-dimensional toric code and X-cube states, uncovering a nontrivial path in phase space that connects them through a subdimensional critical point, which is highly challenging to detect numerically due to the complexity of simulating three-dimensional systems.

cond-mat.str-el↗

arXiv2024

Fractonic Quantum Quench in Dipole-constrained Bosons

We investigate the quench dynamics in the dipolar Bose-Hubbard model (DBHM) in one dimension. The boson hopping is constrained by dipole conservation and show fractonic dynamics. The ground states at large Hubbard interaction $U$ are Mott insulators at integer filling and a period-2 charge density wave (CDW) at half-integer filling. We focus on Mott-to-Mott and CDW-to-CDW quenches and find that dipole correlation spreading shows the light-cone behavior with the Lieb-Robinson (LR) velocity proportional to the dipole kinetic energy $J$ and the square of the density in the case of Mott quench at integer filling. Effective model for post-quench dynamics is constructed under the dilute-dipole approximation and fits the numerical results well. For CDW quench we observe a much reduced LR velocity of order $J^2/U$ and additional periodic features in the time direction. The emergence of CDW ground state and the reduced LR velocity at half-integer filling can both be understood by careful application of the second-order perturbation theory. The oscillatory behavior arises from quantum scars in the quadrupole sector of the spectrum and is captured by a PXP-like model that we derive by projecting the DBHM to the quadrupolar sector of the Hilbert space.

cond-mat.quant-gas↗

arXiv2024

Generating function for projected entangled-pair states

Diagrammatic summation is a common bottleneck in modern applications of projected entangled-pair states, especially in computing low-energy excitations of a two-dimensional quantum many-body system. To solve this problem, here we extend the generating function approach for tensor network diagrammatic summation, a scheme previously proposed in the context of matrix product states. Taking the form of a one-particle excitation, we show that the excited state can be computed efficiently in the generating function formalism, which can further be used in evaluating the dynamical structure factor of the system. Our benchmark results for the spin-$1/2$ transverse-field Ising model and Heisenberg model on the square lattice provide a desirable accuracy, showing good agreement with known results. We then study the spin-$1/2$ $J_1$-$J_2$ model on the same lattice and investigate the dynamical properties of the putative gapless spin liquid phase. We conclude with a discussion on generalizations to multi-particle excitations.

cond-mat.str-el↗

arXiv2023

Ashkin-Teller phase transition and multicritical behavior in a classical monomer-dimer model

We use Monte Carlo simulations and tensor network methods to study a classical monomer-dimer model on the square lattice with a hole (monomer) fugacity $z$, an aligning dimer-dimer interaction $u$ that favors columnar order, and an attractive dimer-dimer interaction $v$ between two adjacent dimers that lie on the same principal axis of the lattice. The Monte Carlo simulations of finite size systems rely on our grand-canonical generalization of the dimer worm algorithm, while the tensor network computations are based on a uniform matrix product ansatz for the eigenvector of the row-to-row transfer matrix that work directly in the thermodynamic limit. The phase diagram has nematic, columnar order and fluid phases, and a nonzero temperature multicritical point at which all three meet. For any fixed $v/u < \infty$, we argue that this multicritical point continues to be located at a nonzero hole fugacity $z_{\rm mc}(v/u) > 0$; our numerical results confirm this theoretical expectation but find that $z_{\rm mc}(v/u) \to 0$ very rapidly as $v/u \to \infty$. Our numerical results also confirm the theoretical expectation that the corresponding multicritical behavior is in the universality class of the four-state Potts multicritical point on critical line of the two-dimensional Ashkin-Teller model.

cond-mat.stat-mech↗

arXiv2023

Cubic ferromagnet and emergent $U(1)$ symmetry on its phase boundary

We study the simplest quantum lattice spin model for the two-dimensional (2D) cubic ferromagnet by means of mean-field analysis and tensor network calculation. While both methods give rise to similar results in detecting related phases, the 2D infinite projected entangled-pair state (iPEPS) calculation provides more accurate values of transition points. Near the phase boundary, moreover, our iPEPS results indicate that it is more difficult to pin down the orientation of magnetic easy axes, and we interpret it as the easy-axis softening. This phenomenon implies an emergence of continuous $U(1)$ symmetry, which is indicated by the low-energy effective model and has been analytically shown by the field theory. Our model and study provide a concrete example for utilizing iPEPS near the critical region, showing that the emergent phenomenon living on the critical points can already be captured by iPEPS with a rather small bond dimension.

cond-mat.str-el↗

arXiv2023

Aspects of $\mathbb{Z}_N$ rank-2 gauge theory in $(2+1)$ dimensions: construction schemes, holonomies, and sublattice one-form symmetries

Rank-2 toric code (R2TC), a prototypical archetype of the discrete rank-2 symmetric gauge theory, has properties that differ from those of the standard toric code. Specifically, it features a blending of UV and IR in its ground state, restricted mobility of its quasiparticles, and variations in the braiding statistics of its quasiparticles based on their position. In this paper, we investigate various aspects of $\mathbb{Z}_N$ rank-2 gauge theory in ${(2+1)}$-dimensional spacetime. Firstly, we demonstrate that $U(1)$ rank-2 gauge theory can arise from ${U(1)\times U(1)}$ rank-1 gauge theory after condensing the gauge charges in a specific way. This construction scheme of $U(1)$ rank-2 gauge theory carries over to the $\mathbb{Z}_N$ case simply by Higgsing $U(1)$ to $\mathbb{Z}_N$, after which the resulting rank-2 gauge theory can be tuned to the R2TC. The holonomy operators of R2TC are readily identified using this scheme and are given clear physical interpretation as the pair creation/annihilation of various monopoles and dipoles. Explicit tensor network construction of the ground states of R2TC are given as two copies of the ground states of Kitaev's toric code that are `sewn together' according to the condensation scheme. In addition, through a similar anyon condensation protocol, we present a double semion version of rank-2 toric code whose flux excitations exhibit restricted mobility and semionic statistics. Finally, we identify the generalized discrete symmetries of the R2TC, which are much more complex than typical 1-form symmetries. They include conventional and unconventional 1-form symmetries, such as framed 1-form symmetries and what we call sublattice 1-form symmetries. Using these, we interpret the R2TC's unique properties (UV/IR mixing, position-dependent braiding, etc.) from the modern perspective of generalized spontaneous symmetry breaking and 't Hooft anomalies.

cond-mat.str-el↗

arXiv2022

Dipole condensates in tilted Bose-Hubbard chains

We study the quantum phase diagram of a Bose-Hubbard chain whose dynamics conserves both boson number and boson dipole moment, a situation which can arise in strongly tilted optical lattices. The conservation of dipole moment has a dramatic effect on the phase diagram, which we analyze by combining a field theory analysis with DMRG simulations. Unlike the conventional Bose-Hubbard model, the phase diagram contains no compressible phases, and is instead dominated by various types of exotic dipolar condensates. We suggest ways by which these condensates can be identified in near-term cold atom experiments.

cond-mat.quant-gas↗

arXiv2022

Topological Thermal Hall Effect of Magnons in Magnetic Skyrmion Lattice

Topological transports of fermions are governed by the Chern numbers of the energy bands lying below the Fermi energy. For bosons, e.g. phonons and magnons in a crystal, topological transport is dominated by the Chern number of the lowest energy band when the band gap is comparable to the thermal energy. Here, we demonstrate the presence of topological transport by bosonic magnons in a lattice of magnetic skyrmions - topological defects formed by a vortex-like texture of spins. We find a distinct thermal Hall signal in the magnetic skyrmion phase of an insulating polar magnet GaV4Se8, identified as the topological thermal Hall effect of magnons governed by the Chern number of the lowest energy band of the magnons in a triangular lattice of magnetic skyrmions. Our findings lay a foundation for studying topological phenomena of other bosonic excitations through thermal Hall probe.

cond-mat.str-el↗

arXiv2022

Variational Tensor Network Operator

We propose a simple and generic construction of the variational tensor network operators to study the quantum spin systems by the synergy of ideas from the imaginary-time evolution and variational optimization of trial wave functions. By applying these operators to simple initial states, accurate variational ground state wave functions with extremely few parameters can be obtained. Furthermore, the framework can be applied to study spontaneously symmetry breaking, symmetry protected topological, and intrinsic topologically ordered phases, and we show that symmetries of the local tensors associated with these phases can emerge directly after the optimization without any gauge fixing. This provides a universal way to identify quantum phase transitions without prior knowledge of the system.

cond-mat.str-el↗

arXiv2022

Field-induced Bose-Einstein condensation and supersolid in the two-dimensional Kondo necklace

The application of an external magnetic field of sufficient strength to a spin system composed of a localized singlet can overcome the energy gap and trigger bosonic condensation and so provide an alternative method to realize exotic phases of matter in real materials. Previous research has indicated that a spin Hamiltonian with on-site Kondo coupling may be the effective many-body Hamiltonian for $\text{Ba}_2\text{NiO}_2\text{(AgSe)}_2$ (BNOAS) and here we study such a Hamiltonian using a tensor network ansatz in two dimensions. Our results unveil a phase diagram which indicates the underlying phases of BNOAS. We propose, in response to the possible doping-induced superconductivity of BNOAS, a fermionic model for further investigation. We hope that our discovery can bring up further interest in both theoretical and experimental researches for related nickelate compounds.

cond-mat.mtrl-sci↗