arXiv subjects

Hyun-Yong Lee

Publications and source records attributed to Hyun-Yong Lee.

36 records · Page 2Linked to original sources

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↗

arXiv2022

Pre-thermalization via self-driving and external driving of extensive subsystems

We investigate the non-equilibrium states of an interacting multi-component quantum system when only an extensive subsystem is quantum-quenched or driven from the ground state. As a concrete example, we consider a system where two XXZ spin chains are coupled to a transverse field Ising (TFI) chain, and only the transverse field in the TFI chain is quantum-quenched or periodically driven in time, starting from an initially ordered state. This system is studied using density matrix renormalization group (DMRG) simulations and various entanglement entropy diagnostics. In the case of quantum quenching, when the transverse field is suddenly switched on to become the largest energy scale, the resulting internal dynamics leads to a pre-thermal steady state with persistent oscillating magnetization (`self-driving') and emergent conservation laws. Upon applying the time-dependent drive to the TFI chain (`external driving'), sufficiently fast drive gives rise to a pre-thermal steady state with finite magnetization, whereas a slow drive generates a high-temperature disordered state. We briefly discuss the experimental implementation of our protocol in organic materials with quantum-tunneling hydrogen atoms.

cond-mat.str-el↗

arXiv2021

Advancing Hybrid Quantum-Classical Algorithms via Mean-Operators

Entanglement in quantum many-body systems is the key concept for future technology and science, opening up a possibility to explore uncharted realms in an enormously large Hilbert space. The hybrid quantum-classical algorithms have been suggested to control quantum entanglement of many-body systems, and yet their applicability is intrinsically limited by the numbers of qubits and quantum operations. Here we propose a theory which overcomes the limitations by combining advantages of the hybrid algorithms and the standard mean-field-theory in condensed matter physics, named as mean-operator-theory. We demonstrate that the number of quantum operations to prepare an entangled target many-body state such as symmetry-protected-topological states is significantly reduced by introducing a mean-operator. We also show that a class of mean-operators is expressed as time-evolution operators and our theory is directly applicable to quantum simulations with $^{87}$Rb neutral atoms or trapped $^{40}$Ca$^+$ ions.

cond-mat.str-el↗

arXiv2021

A Subsystem Ginzburg-Landau and SPT Orders Co-existing on a Graph

We analyze a model demonstrating the co-existence of subsystem symmetry breaking (SSB) and symmetry-protected topological (SPT) order, or subsystem LSPT order for short. Its mathematical origin is the existence of both a subsystem and a local operator, both of which commute with the Hamiltonian but anti-commute between themselves. The reason for the exponential growth of the ground state degeneracy is attributed to the existence of subsystem symmetries, which allows one to define both the Landau order parameter and the SPT-like order for each independent loop.

cond-mat.str-el↗

arXiv2020

Matrix Product Wave Function of the Ground State and Elementary Excitation in the Spin-1/2 Chain

We present a variational matrix product state (vMPS) for the ground state of the spin-1/2 Heisenberg model. The MPS effectively organizes the various dimer configurations, in faithful reflection of the resonating valence bond (RVB) picture of the spin liquid, with the energy only 0.024% higher than the exact value given by Bethe ansatz. Building on the ground-state vMPS, the one-spin wave function is constructed in a simple manner with the dispersion that matches well with the exact spectrum. The vMPS scheme is applied to the family of Hamiltonian extrapolating between the Heisenberg model and the Majumdar-Ghosh model.

cond-mat.str-el↗

arXiv2020

Thermal Hall Effects of Spins and Phonons in Kagome Antiferromagnet Cd-Kapellasite

We have investigated the thermal-transport properties of the kagome antiferromagnet Cd-kapellasite (Cd-K). We find that a field suppression effect on the longitudinal thermal conductivity k_xx sets in below ~25 K, suggesting a large spin contribution k_xx^sp in k_xx. We also find clear thermal Hall signals in the spin liquid phase in all Cd-K samples. The magnitude of the thermal Hall conductivity k_xy shows a significant dependence on the sample's scattering time. On the other hand, the temperature dependence of k_xy is similar in all Cd-K samples; k_xy shows a peak at almost the same temperature of the peak of the phonon thermal conductivity k_xy^ph which is estimated by k_xx at 15 T. These results indicate the presence of a dominant phonon thermal Hall k_xy^ph at 15 T. In addition to k_xy^ph, we find that the field dependence of k_xy at low fields turns out to be non-linear at low temperatures, concomitantly with the appearance of the field suppression of k_xx, indicating the presence of a spin thermal Hall k_xy^sp at low fields. Remarkably, by assembling the k_xx dependene of k_xy^sp data of other kagome antiferromagnets, we find that, whereas k_xy^sp stays a constant in the low-k_xx region, k_xy^sp starts to increase as k_xx does in the high-k_xx region. This k_xx dependence of k_xy^sp indicates the presence of both intrinsic and extrinsic mechanisms in the spin thermal Hall effect in kagome antiferromagnets. Furthermore, both k_xy^ph and k_xy^sp disappear in the antiferromagnetic ordered phase at low fields, showing that phonons alone do not exhibit the thermal Hall effect. A high field above ~7 T induces k_xy^ph, concomitantly with a field-induced increase of k_xx and the specific heat, suggesting a coupling of the phonons to the field-induced spin excitations as the origin of k_xy^ph.

cond-mat.str-el↗

arXiv2020

Entanglement Properties of Disordered Quantum Spin Chains with Long-Range Antiferromagnetic Interactions

We examine the concurrence and entanglement entropy in quantum spin chains with random long-range couplings, spatially decaying with a power-law exponent $α$. Using the strong disorder renormalization group (SDRG) technique, we find by analytical solution of the master equation a strong disorder fixed point, characterized by a fixed point distribution of the couplings with a finite dynamical exponent, which describes the system consistently in the regime $α> 1/2$. A numerical implementation of the SDRG method yields a power law spatial decay of the average concurrence, which is also confirmed by exact numerical diagonalization. However, we find that the lowest-order SDRG approach is not sufficient to obtain the typical value of the concurrence. We therefore implement a correction scheme which allows us to obtain the leading order corrections to the random singlet state. This approach yields a power-law spatial decay of the typical value of the concurrence, which we derive both by a numerical implementation of the corrections and by analytics. Next, using numerical SDRG, the entanglement entropy (EE) is found to be logarithmically enhanced for all $α$, corresponding to a critical behavior with an effective central charge $c = {\rm ln} 2$, independent of $α$. This is confirmed by an analytical derivation. Using numerical exact diagonalization (ED), we confirm the logarithmic enhancement of the EE and a weak dependence on $α$. For a wide range of distances $l$, the EE fits a critical behavior with a central charge close to $c=1$, which is the same as for the clean Haldane-Shastry model with a power-la-decaying interaction with $α=2$. Consistent with this observation, we find using ED that the concurrence shows power law decay, albeit with smaller power exponents than obtained by SDRG.

cond-mat.dis-nn↗

arXiv2020

Anisotropy as a diagnostic test for distinct tensor network wavefunctions of integer and half-integer spin Kitaev quantum spin liquids

Contrasting ground states of quantum magnets with the integer and half-integer spin moments are the manifestation of many-body quantum interference effects. In this work, we investigate the distinct nature of the integer and half-integer spin quantum spin liquids in the framework of the Kitaev's model on the honeycomb lattice. The models with arbitrary spin quantum numbers are not exactly solvable in contrast to the well-known quantum spin liquid solution of the spin-1/2 system. We use the tensor network wavefunctions for the integer and half-integer spin quantum spin liquid states to unveil the important difference between these states. We find that the distinct sign structures of the tensor network wavefunction for the integer and half-integer spin quantum spin liquids are responsible for completely different ground states in the spatially anisotropic limit. Hence the spatial anisotropy would be a useful diagnostic test for distinguishing these quantum spin liquid states, both in the numerical computations and experiments on real materials. We support this discovery via extensive numerics including the tensor network, DMRG, and exact diagonalization computations.

cond-mat.str-el↗

arXiv2020

Construction of Variational Matrix Product States for the Heisenberg Spin-1 Chain

We propose a simple variational wave function that captures the correct ground state energy of the spin-1 Heisenberg chain model to within 0.04\%. The wave function is written in the matrix product state (MPS) form with the bond dimension $D=8$, and characterized by three fugacity parameters. The proposed MPS generalizes the Affleck-Kennedy-Lieb-Tasaki (AKLT) state by dressing it with dimers, trimers, and general $q$-dimers. The fugacity parameters control the number and the average size of the $q$-mers. Furthermore, the $D=8$ variational MPS state captures the ground states of the entire family of bilinear-biquadratic Hamiltonian belonging to the Haldane phase to high accuracy. The 2-4-2 degeneracy structure in the entanglement spectrum of our MPS state is found to match well with the results of density matrix renormalization group (DMRG) calculation, which is computationally much heavier. Spin-spin correlation functions also find excellent fit with those obtained by DMRG.

cond-mat.str-el↗

arXiv2020

Magnetic field induced quantum phases in a tensor network study of Kitaev magnets

Recent discovery of the half quantized thermal Hall conductivity in $α$-RuCl$_3$, a candidate material for the Kitaev spin liquid, suggests the presence of a highly entangled quantum state in external magnetic fields. This field induced phase appears between the low field zig-zag magnetic order and the high field polarized state. Motivated by this experiment, we study possible field induced quantum phases in theoretical models of the Kitaev magnets, using the two dimensional tensor network approach or infinite tensor product states. We find various quantum ground states in addition to the chiral Kitaev spin liquid occupying a small area in the phase diagram. They form a band of emergent quantum phases in an intermediate window of external magnetic fields, somewhat reminiscent of the experiment. We discuss the implications of these results in view of the experiment and previous theoretical studies.

cond-mat.str-el↗

arXiv2020

Abelian and non-Abelian chiral spin liquids in a compact tensor network representation

We provide new insights into the Abelian and non-Abelian chiral Kitaev spin liquids on the star lattice using the recently proposed loop gas (LG) and string gas (SG) states [H.-Y. Lee, R. Kaneko, T. Okubo, N. Kawashima, Phys. Rev. Lett. 123, 087203 (2019)]. Those are compactly represented in the language of tensor network. By optimizing only one or two variational parameters, accurate ansatze are found in the whole phase diagram of the Kitaev model on the star lattice. In particular, the variational energy of the LG state becomes exact(within machine precision) at two limits in the model, and the criticality at one of those is analytically derived from the LG feature. It reveals that the Abelian CSLs are well demonstrated by the short-ranged LG while the non-Abelian CSLs are adiabatically connected to the critical LG where the macroscopic loops appear. Furthermore, by constructing the minimally entangled states and exploiting their entanglement spectrum and entropy, we identify the nature of anyons and the chiral edge modes in the non-Abelian phase with the Ising conformal field theory.

cond-mat.str-el↗

arXiv2019

Tensor network wavefunction of $S=1$ Kitaev spin liquids

Recently there has been a great interest in understanding quantum spin liquid phases with varying spin magnitude, partly due to possible material realizations. A number of recent numerical computations suggest that the ground state of the S=1 Kitaev model may be a quantum spin liquid in analogy to the renowned $S$=$1/2$ model. On the other hand, the nature of the ground state remains elusive since the $S$=$1$ model is not exactly solvable in contrast to the $S$=$1/2$ model. In this work, we construct a tensor network ground state wavefunction for the S=1 Kitaev model, which is explicitly written in terms of physical spin operators. We explain how this class of wavefunctions can be successfully used for variational computations and compare the outcomes to known results on finite size systems. We establish the existence of distinct topological sectors on torus by constructing the minimally entangled states in the degenerate ground state manifold and evaluating topological entanglement entropy. Our results suggest that the ground state of the S=1 Kitaev model is a gapped quantum spin liquid with Z2 gauge structure and Abelian quasiparticles.

cond-mat.str-el↗

arXiv2019

Spin-one bilinear-biquadratic model on a star lattice

We study the ground-state phase diagram of the $S=1$ bilinear-biquadratic model\,(BLBQ) on the star lattice with the state-of-art tensor network algorithms. The system has five phases: the ferromagnetic, anti-ferromagnetic, ferroquadrupolar, and spin-liquid phases. The phases and their phase boundaries are determined by examining various local observables, correlation functions and transfer matrices exhaustively. The spin liquid phase, which is the first quantum disordered phase found in two-dimensional BLBQ model, is gapped and devoid of any conventional long-range order. It is also characterized by fixed-parity virtual bonds in the tensor network formalism, analogous to the Haldane phase, while the parity varies depending on the location of the bond.

cond-mat.str-el↗

arXiv2019

Gapless Kitaev Spin Liquid to Classical String Gas through Tensor Networks

We provide a framework for understanding the gapless Kitaev spin liquid (KSL) in the language of tensor network(TN). Without introducing Majorana fermion, most of the features of the KSL including the symmetries, gauge structure, criticality and vortex-freeness are explained in a compact TN representation. Our construction reveals a hidden string gas structure of the KSL. With only two variational parameters to adjust, we obtain an accurate KSL ansatz with the bond dimension D = 8 in a compact form, where the energy is about 0.007% higher than the exact one. In addition, the opening of gap and non-Abelian phase driven by a magnetic field are naturally understood in our construction.

cond-mat.str-el↗

arXiv2019

Magnetic Field Induced Competing Phases in Spin-Orbital Entangled Kitaev Magnets

There has been a great interest in magnetic field induced quantum spin liquids in Kitaev magnets after the discovery of neutron scattering continuum and half quantized thermal Hall conductivity in the material $α$-RuCl$_3$. In this work, we provide a semiclassical analysis of the relevant theoretical models on large system sizes, and compare the results to previous studies on quantum models with small system sizes. We find a series of competing magnetic orders with fairly large unit cells at intermediate magnetic fields, which are most likely missed by previous approaches. We show that quantum fluctuations are typically strong in these large unit cell orders, while their magnetic excitations may resemble a scattering continuum and give rise to a large thermal Hall conductivity. Our work provides an important basis for a thorough investigation of emergent spin liquids and competing phases in Kitaev magnets.

cond-mat.str-el↗

arXiv2018

Spin Thermal Hall Conductivity of a Kagomé Antiferromagnet

A clear thermal Hall signal ($κ_{xy}$) was observed in the spin liquid phase of the $S=1/2$ kagomé antiferromagnet Ca kapellasite (CaCu$_3$(OH)$_6$Cl$_2\cdot 0.6$H$_2$O). We found that $κ_{xy}$ is well reproduced, both qualitatively and quantitatively, using the Schwinger-boson mean-field theory with the Dzyaloshinskii--Moriya interaction of $D/J \sim 0.1$. In particular, $κ_{xy}$ values of Ca kapellasite and those of another kagomé antiferromagnet, volborthite, converge to one single curve in simulations modeled using Schwinger bosons, indicating a common temperature dependence of $κ_{xy}$ for the spins of a kagomé antiferromagnet.

cond-mat.str-el↗

arXiv2018

Tensor-Ring Decomposition with Index-Splitting

Tensor-ring decomposition of tensors plays a key role in various applications of tensor network representation in physics as well as in other fields. In most heuristic algorithms for the tensor-ring decomposition, one encounters the problem of local-minima trapping. Particularly, the minima related to the topological structure in the correlation are hard to escape. Therefore, identification of the correlation structure, somewhat analogous to finding matching ends of entangled strings, is the task of central importance. We show how this problem naturally arises in physical applications, and present a strategy for winning this string-pull game.

physics.comp-ph↗

arXiv2017

Disordered Quantum Spin Chains with Long-Range Antiferromagnetic Interactions

We investigate the magnetic susceptibility $χ(T)$ of quantum spin chains of $N=1280$ spins with power-law long-range antiferromagnetic coupling as a function of their spatial decay exponent $α$ and cutoff length $ξ$. The calculations are based on the strong disorder renormalization method which is used to obtain the temperature dependence of $χ(T)$ and distribution functions of couplings at each renormalization step. For the case with only algebraic decay ($ ξ= \infty$) we find a crossover at $α^*=1.066$ between a phase with a divergent low-temperature susceptibility $χ(T\rightarrow 0) $ for $α> α^*$ to a phase with a vanishing $χ(T\rightarrow 0) $ for $α< α^*$. For finite cutoff lengths $ξ$, this crossover occurs at a smaller $α^*(ξ)$. Additionally we study the localization of spin excitations for $ ξ= \infty$ by evaluating the distribution function of excitation energies and we find a delocalization transition that coincides with the opening of the pseudo-gap at $α_c=α^*$.

cond-mat.dis-nn↗