arXiv subjects

Sam Young Cho

Publications and source records attributed to Sam Young Cho.

At least 19 recordsLinked to original sources

arXiv2024

Quantum entanglement entropy and Tomonaga-Luttinger liquid to liquid transition in biquadratic spin-1 XY chain with rhombic single-ion anisotropy

Quantum phase transitions (QPTs) are investigated in biquadratic spin-$1$ XY chain with rhombic single-ion anisotropy by using the ground state energy (GE), the bipartite entanglement entropy (BEE), and the mutual information (MI). It turns out that there are three spin nematic phases and two Tomonaga-Luttinger (TL) liquid phases with the central charge $c = 1$. The TL Liquid phases emerge roughly for biquadratic interaction strength two times stronger than the absolute value of the single-ion anisotropy. The GE and the derivatives up to the second order reveal a first-order QPT between spin nematic ferroquarupole (FQ) phases but cannot capture an evident signal of QPTs between the spin nematic phases and the TL Liquid phases as well as QPT between the two TL liquid phases. The TL liquid-to-liquid transition point features a highly degenerate state and the spin-block entanglement entropy increases logarithmically with block size. The BEE exhibits a divergent or convergent behavior identifying the TL Liquid or spin nematic FQ phases, respectively. Similarly, the MI and the spin-spin correlation are shown to decay algebraically or exponentially with increasing the lattice distance in the TL Liquid or spin nematic FQ phases, respectively. In the TL liquid phase, the exponents $\eta_I$ and $\eta_z$ of the MI and the spin-spin correlation vary with the interaction parameter of the biquadratic interaction strength and the rhombic single-ion anisotropy and satisfy the relationship of $\eta_z <\eta_I$. Such changes of characteristic behavior of the BEE, the MI and the spin-spin correlation indicate an occurrence of the Berezinskii-Kosterlitz-Thouless (BKT)-type QPT between the TL Liquid phase and the spin nematic FQ phase. The staggered spin fluctuation $\langle S^x S^y \rangle$ is shown to play a significant role for the emergence of the TL liquid phase and thus give rise to the BKT-type QPT.

cond-mat.str-el↗

arXiv2024

Wigner-Yanase skew information, quantum entanglement and spin nematic quantum phase transitions in biquadratic spin-1 and spin-2 XY chains with single-ion anisotropies

Quantum phase transitions (QPTs) between uniaxial or biaxial spin nematic (SN) phases are investigated in biquadratic spin-1 and spin-2 XY infinite chains with the rhombic- and uniaxial-type single-ion anisotropies. Systematic discussions of distinctive singular behaviors are made to classify various types of QPT from one SN state to the other SN state in using the Wigner-Yanase skew information (WYSI), the bipartite entanglement entropy (BEE), and the quadrupole moments (QMs). For the spin-1 system with the three uniaxial SN phases, we find that a discontinuous QPT, signaled by discontinuous behaviors of all the considered WYSI, BEE, and QMs, occurs from the z-ferroquadrupole phase (FQP) to the x- or y-FQPs, while a continuous QPT occurs between the x- and y-FQPs. The central charge in the continuous QPT line is estimated as $c \simeq 1$ from the BEE. Compared to the spin-1 system, depending on a given strength of the uniaxial-type single-ion anisotropy, the spin-2 system undergoes four different types of QPTs between the two biaxial SN phases as the rhombic-type anisotropy varies: the quantum crossovers, connecting the two orthogonal biaxial SN states adiabatically without an explicit phase transition, the continuous and the discontinuous QPTs, and the SN to magnetic transitions via the antiferromagnetic phase (AFP). In a sharp contrast to the spin-1 system, for the transitions between the two biaxial SN phases, the discontinuous transition line is classified as a topological phase characterized by a doubly degenerate entanglement spectrum and a string order parameter defined by the Cartan generator of the $\mathrm{SO}(5)$ symmetry group in spin-2 systems, while the continuous QPT is advocated by the central charge $c \simeq 1$. Whereas the QPT lines with $c \simeq 1/2$ indicate that the transition between the biaxial SN phase and the AFP belongs to the Ising universality class.

cond-mat.str-el↗

arXiv2020

Quantum coherence and spin nematic to nematic quantum phase transitions in biquadratic spin-1 and -2 XY chains with rhombic single-ion anisotropy

We investigate quantum phase transitions and quantum coherence in infinite biquadratic spin-1 and -2 XY chains with rhombic single-ion anisotropy. All considered coherence measures such as the $l_1$ norm of coherence, the relative entropy of coherence, and the quantum Jensen-Shannon divergence, and the quantum mutual information show consistently that singular behaviors occur for the spin-1 system, which enables to identity quantum phase transitions. For the spin-2 system, the relative entropy of coherence and the quantum mutual information properly detect no singular behavior in the whole system parameter range, while the $l_1$ norm of coherence and the quantum Jensen-Shannon divergence show a conflicting singular behavior of their first-order derivatives. Examining local magnetic moments and spin quadrupole moments lead to the explicit identification of novel orderings of spin quadrupole moments with zero magnetic moments in the whole parameter space. We find the three uniaxial spin nematic quadrupole phases for the spin-1 system and the two biaxial spin nematic phases for the spin-2 system. For the spin-2 system, the two orthogonal biaxial spin nematic states are connected adiabatically without an explicit phase transition, which can be called quantum crossover. The quantum crossover region is estimated by using the quantum fidelity. Whereas for the spin-1 system, the two discontinuous quantum phase transitions occur between three distinct uniaxial spin nematic phases. We discuss the quantum coherence measures and the quantum mutual information in connection with the quantum phase transitions including the quantum crossover.

cond-mat.str-el↗

arXiv2020

Critical exponents of block-block mutual information in one-dimensional infinite lattice systems

We study the mutual information between two lattice-blocks in terms of von Neumann entropies for one-dimensional infinite lattice systems. Quantum $q$-state Potts model and transverse field spin-$1/2$ XY model are considered numerically by using the infinite matrix product state (iMPS) approach. As a system parameter varies, block-block mutual informations exhibit a singular behavior that enables to identify critical points for quantum phase transition. As happens with the von Neumann entanglement entropy of a single block, at the critical points, the block-block mutual information between the two lattice-blocks of $\ell$ contiguous sites equally partitioned in a lattice-block of $2\ell$ contiguous sites shows a logarithmic leading behavior, which yields the central charge $c$ of the underlying conformal field theory. As the separation between the two lattice-blocks increases, the mutual information reveals a consistent power-law decaying behavior for various truncation dimensions and lattice-block sizes. The critical exponent of block-block mutual information in the thermodynamic limit is estimated by extrapolating the exponents of power-law decaying regions for finite truncation dimensions. For a given lattice-block size $\ell$, the critical exponents for the same universality classes seem to have very close values each other. Whereas the critical exponents have different values to a degree of distinction for different universality classes. As the lattice-block size becomes bigger, the critical exponent becomes smaller.

cond-mat.str-el↗

arXiv2020

Spin operators and representations of the Poincaré group

We present the rigorous derivation of covariant spin operators from a general linear combination of the components of the Pauli-Lubanski vector. It is shown that only two spin operators satisfy the spin algebra and transform properly under the Lorentz transformation, which admit the two inequivalent finite-dimensional representations for the Lorentz generators through the complexification of the $SU(2)$ group. In case that the Poincaré group is extended by parity operation, the spin operator in the direct sum representation of the two inequivalent representations, called the new spin distinguished from the Dirac spin, is shown to be equivalent to axial and Hermitian spin operators for particle and antiparticle. We have shown that for spin $1/2$, the Noether conserved current for a rotation can be divided into separately conserved orbital and spin part for the new spin, unlike for the Dirac spin. This implies that the new spin not the Dirac spin provides good quantum observables.

physics.gen-ph↗

arXiv2019

Singularity of relativistic vortex beam and proper relativistic observables

We have studied the phase singularity of the relativistic vortex beams for the two sets of relativistic operators. One includes the new spin and orbital angular momentum (OAM) operators, which is derived from the parity-extended Poincaré group, and the other is composed of the (usual) Dirac spin and OAM operators. The first set predicts the same singular circulation as the nonrelativistic vortex beams. On the other hand, the second set anticipates that the singularity of the circulation is spin orientation-dependent and can be disappeared especially for relativistic paraxial electron beam with spin parallel to the propagating direction. These contradistinctive predictions suggest the relativistic electron beam experiment with spin-polarized electrons for the first time to answer the long-standing fundamental question, i.e., what are the proper relativistic observables, raised from the beginning of relativistic quantum mechanics since the discovery of the Dirac equation.

quant-ph↗

arXiv2018

Universal scaling relationship between classical and quantum correlations in critical quantum spin chains

We numerically investigate classical and quantum correlations in one-dimensional quantum critical systems. The infinite matrix product state (iMPS) representation is employed in order to consider an infinite-size spin chain. By using the infinite time-evolving block decimation algorithm, iMPS ground state wave functions are obtained at critical points for the transverse-field spin-$1/2$ XY model. From the ground state wave functions, we calculate classical and quantum correlations and mutual information. All of the correlations are found to exhibit a power-law decay with the increments of the lattice distance for both the transition lines of the Ising universality class and the Gaussian universality class. Such power-law scaling behaviors of the correlations manifest the existence of diversing correlation lengths, which means scale invariance. The critical features of the correlations can be characterized by introducing a critical exponent of the power-law decaying correlations. Similar to the critical exponent $η$ of the spin-spin correlation for the universality classes in the transverse-field XY model, we calculate the critical exponents of the two-spin classical and quantum correlations as well as that of the corresponding mutual information. All of the correlations have the same critical exponents, i.e., $η^{I}=η^{C}=η^{D}$ at a critical point, where the superscripts $I$, $C$, and $D$ stand for mutual information, classical correlation, and quantum correlation, respectively. Furthermore, the critical exponent $η$ of the spin-spin correlation is shown to relate to $η= η^α/2$ with $α\in \{ I, C, D\}$.

cond-mat.str-el↗

arXiv2017

Finite-temperature fidelity and von Neumann entropy in the honeycomb spin lattice with quantum Ising interaction

The finite temperature phase diagram is obtained for an infinite honeycomb lattice with spin-$1/2$ Ising interaction $J$ by using thermal-state fidelity and von Neumann entropy based on the infinite projected entangled pair state algorithm with ancillas. % The tensor network representation of the fidelity, which is defined as an overlap measurement between two thermal states, is presented for thermal states on the honeycomb lattice. % We show that the fidelity per lattice site and the von Neumann entropy can capture the phase transition temperatures for applied magnetic field, consistent with the transition temperatures obtained via the transverse magnetizations, which indicates that a continuous phase transition occurs in the system. In the temperature-magnetic field plane, the phase boundary is found to have the functional form $(k_BT_c)^2 + h_c^2/2 = a J^2$ with a single numerical fitting coefficient $a = 2.298$, where $T_c$ and $h_c$ are the critical temperature and field with the Boltzmann constant $k_B$. For the quantum state at zero temperature, this phase boundary function gives the critical field estimate $h_c = \sqrt{2a} J \simeq 2.1438 J$, consistent with the known value $h_c = 2.13250(4)\, J$ calculated from a Cluster Monte Carlo approach. The critical temperature in the absence of magnetic field is estimated as $k_BT_c = \sqrt{a}J \simeq 1.5159\, J$, consistent with the exact result $k_BT_c = 1.51865...\, J$.

cond-mat.str-el↗

arXiv2016

Entanglement entropy and massless phase in the antiferromagnetic three-state quantum chiral clock model

The von Neumann entanglement entropy is used to estimate the critical point $h_c/J \simeq 0.143(3)$ of the mixed ferro-antiferromagnetic three-state quantum Potts model $H = \sum_i [ J ( X_i X_{i+1}^{\,2} + X_i^{\,2} X_{i+1} ) - h\, R_i ]$, where $X_i$ and $R_i$ are standard three-state Potts spin operators and $J>0$ is the antiferromagnetic coupling parameter. This critical point value gives improved estimates for two Kosterlitz-Thouless transition points in the antiferromagnetic ($β< 0$) region of the $Δ$--$β$ phase diagram of the three-state quantum chiral clock model, where $Δ$ and $β$ are, respectively, the chirality and coupling parameters in the clock model. These are the transition points $β_c \simeq - 0.143(3)$ at $Δ= \frac12$ between incommensurate and commensurate phases and $β_c \simeq - 7.0(1)$ at $Δ= 0$ between disordered and incommensurate phases. The von Neumann entropy is also used to calculate the central charge $c$ of the underlying conformal field theory in the massless phase $h \le h_c$. The estimate $c \simeq 1$ in this phase is consistent with the known exact value at the particular point $h/J = -1$ corresponding to the purely antiferromagnetic three-state quantum Potts model. The algebraic decay of the Potts spin-spin correlation in the massless phase is used to estimate the continuously varying critical exponent $η$.

cond-mat.stat-mech↗

arXiv2016

Spin Operators for Massive Particles

Since the discovery a century ago, spin describing the intrinsic angular momentum of massive elementary particles has exposed its nature and significant roles in wide ranges of (relativistic) quantum phenomena and practical applications for future quantum technology. Emerging inconsistencies have also disclosed its telltale incomplete description. Finding relativistic spins (operators) of massive particles is a long-standing fundamental problem from the beginning of relativistic quantum mechanics. Here we present the rigorous derivation and the representation of spin operators from the spacetime symmetry. The covariant parity operation, defined by the spin operators, naturally leads to a fundamental equation equivalent to the covariant Dirac equation, which manifests existent relativistic spins. Proper understanding position operator in the Dirac theory on account of the spin operator through total angular momentum predicts no Zitterbewegung as well as conserving orbital and spin currents. The spin operators can be applicable for unraveling the inconsistencies and for exploring unveiled physics of massive particles.

quant-ph↗

arXiv2016

Geometric entanglement and quantum phase transitions in two-dimensional quantum lattice models

Geometric entanglement(GE), as a measure of multipartite entanglement, has been investigated as a universal tool to detect phase transitions in quantum many-body lattice models. We outline a systematic method to compute GE for two-dimensional (2D) quantum many-body lattice models based on the translational invariant structure of infinite projected entangled pair state (iPEPS) representations. By employing this method, the $q$-state quantum Potts model on the square lattice with $q \in \{2, 3 ,4, 5\}$ is investigated as a prototypical example. Further, we have explored three 2D Heisenberg models, such as the spin-$\frac{1}{2}$ XXX and antiferromagnetic anisotropic XYX models in an external magnetic field, and the spin-1 antiferromagnetic XXZ model. We find that continuous GE does not guarantee a continuous phase transition across a phase transition point. We observe and thus classify three different types of continuous GE across a phase transition point: (i) GE is continuous with maximum value at the transition point and the phase transition is continuous, (ii) GE is continuous with maximum value at the transition point but the phase transition is discontinuous, and (iii) GE is continuous with non-maximum value at the transition point and the phase transition is continuous. For the models under consideration we find that the second and the third types are related to a point of dual symmetry and a fully polarized phase, respectively.

cond-mat.str-el↗

arXiv2015

The antiferromagnetic cross-coupled spin ladder: quantum fidelity and tensor networks approach

We investigate the phase diagram of the cross-coupled Heisenberg spin ladder with antiferromagnetic couplings. For this model there have been conflicting results for the existence of the columnar dimer phase, which was predicted on the basis of weak coupling field theory renormalisation group arguments. The numerical work on this model has been based on various approaches, including exact diagonalization, series expansions and density-matrix renormalization group calculations. Using the recently developed tensor network states and ground-state fidelity approach for quantum spin ladders we find no evidence for the existence of the columnar dimer phase. We also provide an argument based on the symmetry of the Hamiltonian which suggests that the phase diagram for antiferromagnetic couplings consists of a single line separating the rung-singlet and Haldane phases.

cond-mat.str-el↗

arXiv2015

Quantum fidelity approach to detecting quantum phases: revisiting the bond alternating Ising chain

We demonstrate the quantum fidelity approach for exploring and mapping out quantum phases. As a simple model exhibiting a number of distinct quantum phases, we consider the alternating-bond Ising chain using the infinite time evolving block decimation method in the infinite matrix product state representation. Examining the quantum fidelity with an arbitrary reference state in the whole range of the interaction parameters leads to the explicit detection of the doubly degenerate groundstates, indicating a $Z_2$ broken symmetry. The discontinuities of the fidelity indicate a first-order quantum phase transition between the four ordered phases. In order to characterize each phase, based on the spin configurations from the spin correlations, even and odd antiferromagnetic order parameters are introduced. The four defined local order parameters are shown to characterize each phase and to exhibit first-order quantum phase transitions between the ordered phases.

quant-ph↗

arXiv2015

Are degenerate groundstates induced by spontaneous symmetry breakings in quantum phase transitions?

Recently, emergent symmetry is one of fast-growing intriguing issues in many-body systems. Its roles and consequential physics have not been well understood in quantum phase transitions. Emergent symmetry of degenerate groundstates is discussed in possible connection to spontaneous symmetry breaking within the Landau theory. For a clear discussion, a quantum spin-$1/2$ plaquette chain system is shown to have rich emergent symmetry phenomena in its groundstates. A covering symmetry group over all emergent symmetries responsible for degenerate groundstates in the plaquette chain system is found to correspond to a largest common symmetry group of constituent Hamiltonians describing the plaquette system. Consequently, this result suggests that, as a guiding symmetry principle in quantum phase transitions, {\it degenerate groundstates are induced by a spontaneous breaking of symmetries belonging to a largest common symmetry group of continent Hamiltonians describing a given system but can have more symmetries than the largest common symmetry}.

cond-mat.stat-mech↗

arXiv2014

Degenerate groundstates and multiple bifurcations in a two-dimensional q-state quantum Potts model

We numerically investigate the two-dimensional q-state quantum Potts model on the infinite square lattice by using the infinite projected entangled-pair state (iPEPS) algorithm. We show that the quantum fidelity, defined as an overlap measurement between an arbitrary reference state and the iPEPS groundstate of the system, can detect q-fold degenerate groundstates for the Zq broken-symmetry phase. Accordingly, a multiple-bifurcation of the quantum groundstate fidelity is shown to occur as the transverse magnetic field varies from the symmetry phase to the broken-symmetry phase, which means that a multiple-bifurcation point corresponds to a critical point. A (dis-)continuous behavior of quantum fidelity at phase transition points characterizes a (dis-)continuous phase transition. Similar to the characteristic behavior of the quantum fidelity, the magnetizations, as order parameters, obtained from the degenerate groundstates exhibit multiple bifurcation at critical points. Each order parameter is also explicitly demonstrated to transform under the subgroup of the Zq symmetry group. We find that the q-state quantum Potts model on the square lattice undergoes a discontinuous (first-order) phase transition for q = 3 and q = 4, and a continuous phase transition for q = 2 (the 2D quantum transverse Ising model).

cond-mat.str-el↗

arXiv2013

Comment on "Aharonov-Casher and Scalar Aharonov-Bohm Topological Effects"

In this Comment we point out (i) that the Hamiltonian, Eq. (17) in the Letter(Phys. Rev. Lett. 108, 070405 (2012)), is not a relativistic Hamiltonian, (ii) then that the conditions in the Letter are irrelevant for a topological AC and SAB effects, and (iii) conclusively that the non-relativistic Hamiltonian employed by Peshkin and Lipkin (Phys. Rev. Lett. 74, 2847 (1995)) has the same $U(1)_{mm}$ gauge structure for a fixed spin and then is not wrong, but their incorrect interpretation of the spin autocorrelations led to the incorrect conclusion.

cond-mat.mes-hall↗

arXiv2013

Long-range string orders and topological quantum phase transitions in the one-dimensional quantum compass model

In order to investigate the quantum phase transition in the one-dimensional quantum compass model, we numerically calculate non-local string correlations, entanglement entropy, and fidelity per lattice site by using the infinite matrix product state representation with the infinite time evolving block decimation method. In the whole range of the interaction parameters, we find that the four distinct string orders characterize the four different Haldane phases and the topological quantum phase transition occurs between the Haldane phases. The critical exponents of the string order parameters β=1/8 and the cental charges c=1/2 at the critical points show that the topological phase transitions between the phases belong to an Ising type of universality classes. In addition to the string order parameters, the singularities of the second derivative of the ground state energies per site, the continuous and singular behaviors of the von Neumann entropy, and the pinch points of the fidelity per lattice site manifest that the phase transitions between the phases are of the second-order, in contrast to the first-order transition suggested in pervious studies.

cond-mat.str-el↗

arXiv2013

Bond-Alternation-Induced Topological Quantum Gaussian Transition and Topological Quantum Crossover in Ising Chains with the Dzyaloshinskii-Moriya Interaction

Non-local orders, entanglement entropy, and quantum fidelity are investigated in an infinite-size bond-alternating Ising chain with the Dzyaloshinskii-Moriya interaction by employing the infinite matrix product state representation with the infinite time evolving block decimation method. Directly computing two distinct types of finite string correlations for very large lattice distances, in contrast to an extrapolated extreme value for finite size chains, reveals two topologically ordered phases. As the bond alternation varies, a topological quantum phase transition with continuously variable critical exponents along the phase boundary occurs between the two Haldane phases for the Dzyaloshinskii-Moriya interaction stronger than the Ising interaction, while a topological quantum crossover between them happens through an intermediate antiferromagentic phase demonstrated with the quantum fidelity for the Dzyaloshinskii-Moriya interaction weaker than the Ising interaction. The critical exponents of the order parameters and the central charges from the entanglement entropy quantify the universality classes of the phase transition points. Anisotropic Heisenberg types of spin chains with bond alternations are finally discussed to share the same criticality.

cond-mat.str-el↗