arXiv subjects

Wen-Jia Rao

Publications and source records attributed to Wen-Jia Rao.

13 recordsLinked to original sources

arXiv2022

Power-Law Random Banded Matrix Ensemble as the Effective Model for Many-Body Localization Transition

We employ the power-law random band matrix (PRBM) ensemble with single tuning parameter $μ$ as the effective model for many-body localization (MBL) transition in random spin systems. We show the PRBM accurately reproduce the eigenvalue statistics on the entire phase diagram through the fittings of high-order spacing ratio distributions $P(r^{(n)})$ as well as number variance $Σ^{2}(l)$, in systems both with and without time-reversal symmetry. For the properties of eigenvectors, it's shown the entanglement entropy of PRBM displays an evolution from volume-law to area-law behavior which signatures an ergodic-MBL transition, and the critical exponent is found to be $ν=0.83\pm 0.15$, close to the value obtained in 1D physical model by exact diagonalization while the computational cost here is much less.

cond-mat.dis-nn↗

arXiv2022

Approaching Thouless Energy and Griffiths Regime in Random Spin Systems By Singular Value Decomposition

We employ singular value decomposition (SVD) to study the eigenvalue spectra of random spin systems. By SVD, eigenvalue spectrum is decomposed into orthonormal modes $W_k$ with weight $λ_k$. We show that the scree plot ($λ_k$ with respect to $k$) in the ergodic phase contains two branches that both follow power-law $λ_k\sim k^{-α}$ but with different exponents $α$. By evaluating $W_k$, it's verified the part of $λ_k $ with $k>k_{\text{Th}}$ is universal that follows random matrix theory, where $k_{\text{Th}}$ is related to the Thouless energy. We further demonstrate that $α$ corresponds only to the exponential part of the level spacing distribution while being insensitive to the level repulsion, or equivalently the system's symmetry. Consequently, $α$ gives an underestimation for the many-body localization transition point, which suggests a non-ergodic behavior that may be attributed to the Griffiths regime.

cond-mat.dis-nn↗

arXiv2021

Random Matrix Model for Eigenvalue Statistics in Random Spin Systems

We propose a working strategy to describe the eigenvalue statistics of random spin systems along the whole phase diagram with thermal to many-body localization (MBL) transition. Our strategy relies on two random matrix (RM) models with well-defined matrix construction, namely the mixed (Brownian) ensemble and Gaussian $β$ ensemble. We show both RM models are capable of capturing the lowest-order level correlations during the transition, while the deviations become non-negligible when fitting higher-order ones. Specifically, the mixed ensemble will underestimate the longer-range level correlations, while the opposite is true for $β$ ensemble. Strikingly, a simple average of these two models gives nearly perfect description of the eigenvalue statistics at all disorder strengths, even around the critical region, which indicates the interaction range and strength between eigenvalue levels are the two dominant features that are responsible for the phase transition.

cond-mat.dis-nn↗

arXiv2021

Critical Level Statistics at the Many-Body Localization Transition Region

We study the critical level statistics at the many-body localization (MBL) transition region in random spin systems. By employing the inter-sample randomness as indicator, we manage to locate the MBL transition point in both orthogonal and unitary models. We further count the $n$-th order gap ratio distributions at the transition region up to $n=4$, and find they fit well with the short-range plasma model (SRPM) with inverse temperature $β=1$ for orthogonal model and $β=2$ for unitary. These critical level statistics are argued to be universal by comparing results from systems both with and without total $S_{z}$ conservation. We also point out that these critical distributions can emerge from the spectrum of a Poisson ensemble, which indicates the thermal-MBL transition point is more affected by the MBL phase rather than thermal phase.

cond-mat.dis-nn↗

arXiv2021

Scaling of the Reduced Energy Spectrum of Random Matrix Ensemble

We study the reduced energy spectrum $\{E_{i}^{(n)}\}$, which is constructed by picking one level from every $n$ levels of the original spectrum $\{E_{i}\}$, in a Gaussian ensemble of random matrix with Dyson index $β\in \left( 0,\infty \right) $. It's shown $\{E_{i}^{(n)}\}$ bears the same form of probability distribution as $\{E_{i}\}$ with a rescaled parameter $γ=\frac{n(n+1)}{2}β+n-1$. Notably, the $n$-th order level spacing and non-overlapping gap ratio in $\{E_{i}\}$ become the lowest-order ones in $\{E_{i}^{(n)}\}$, hence their distributions will rescale in an identical way. Numerical evidences are provided by simulating random spin chain as well as modelling random matrices. Our results establish the higher-order spacing distributions in random matrix ensembles beyond GOE,GUE,GSE, and reveals a hierarchy of structures hidden in the energy spectrum.

cond-mat.dis-nn↗

arXiv2020

Higher-order level spacings in random matrix theory based on Wigner's conjecture

The distribution of higher order level spacings, i.e. the distribution of $\{s_{i}^{(n)}=E_{i+n}-E_{i}\}$ with $n\geq 1$ is derived analytically using a Wigner-like surmise for Gaussian ensembles of random matrix as well as Poisson ensemble. It is found $s^{(n)}$ in Gaussian ensembles follows a generalized Wigner-Dyson distribution with rescaled parameter $α=νC_{n+1}^2+n-1$, while that in Poisson ensemble follows a generalized semi-Poisson distribution with index $n$. Numerical evidences are provided through simulations of random spin systems as well as non-trivial zeros of Riemann zeta function. The higher order generalizations of gap ratios are also discussed.

cond-mat.dis-nn↗

arXiv2020

Learning What a Machine Learns in a Many-Body Localization Transition

We employ a convolutional neural network to explore the distinct phases in random spin systems with the aim to understand the specific features that the neural network chooses to identify the phases. With the energy spectrum normalized to the bandwidth as the input data, we demonstrate that a network of the smallest nontrivial kernel width selects level spacing as the signature to distinguish the many-body localized phase from the thermal phase. We also study the performance of the neural network with an increased kernel width, based on which we find an alternative diagnostic to detect phases from the raw energy spectrum of such a disordered interacting system.

cond-mat.dis-nn↗

arXiv2018

Identifying Product Order with Restricted Boltzmann Machines

Unsupervised machine learning via a restricted Boltzmann machine is an useful tool in distinguishing an ordered phase from a disordered phase. Here we study its application on the two-dimensional Ashkin-Teller model, which features a partially ordered product phase. We train the neural network with spin configuration data generated by Monte Carlo simulations and show that distinct features of the product phase can be learned from non-ergodic samples resulting from symmetry breaking. Careful analysis of the weight matrices inspires us to define a nontrivial machine-learning motivated quantity of the product form, which resembles the conventional product order parameter.

cond-mat.dis-nn↗

arXiv2016

Emergent infinite-randomness fixed points from the extensive random bipartitions of the spin-1 Affleck-Kennedy-Lieb-Tasaki topological state

Quantum entanglement under an extensive bipartition can reveal the critical boundary theory of a topological phase in the parameter space. In this study we demonstrate that the infinite-randomness fixed point for spin-1/2 degrees of freedom can emerge from an extensive random bipartition of the spin-1 Affleck-Kennedy-Lieb-Tasaki chain. The nested entanglement entropy of the ground state of the reduced density matrix exhibits a logarithmic scaling with an effective central charge $\tilde{c} = 0.72 \pm 0.02 \approx \ln 2$. We further discuss, in the language of bulk quantum entanglement, how to understand all phase boundaries and the surrounding Griffiths phases for the antiferromagnetic Heisenberg spin-1 chain with quenched disorder and dimerization.

cond-mat.str-el↗

arXiv2016

Quantum antiferromagnetic Heisenberg half-odd integer spin model as the entanglement Hamiltonian of the integer spin Affleck-Kennedy-Lieb-Tasaki states

Applying a symmetric bulk bipartition to one-dimensional Affleck-Kennedy-Lieb-Tasaki valence bond solid (VBS) states for the integer spin-S Haldane gapped phase, we can create an array of fractionalized spin-S/2 edge states with the super unit cell $l$ in the reduced bulk system, and the topological properties encoded in the VBS wave functions can be revealed. The entanglement Hamiltonian (EH) with $l=even$ corresponds to the quantum antiferromagnetic Heisenberg spin-S/2 model. For the even integer spins, the EH still describes the Haldane gapped phase. For the odd integer spins, however, the EH just corresponds to the quantum antiferromagnetic Heisenberg half-odd integer spin model with spinon excitations, characterizing the critical point separating the topological Haldane phase from the trivial gapped phase. Our results thus demonstrate that the topological bulk property not only determines its fractionalized edge states, but also the quantum criticality associated with the topological phase, where the elementary excitations are precisely those fractionalized edge degrees of freedom confined in the bulk of the topological phase.

cond-mat.str-el↗

arXiv2016

SU(3) quantum critical model emerging from a spin-1 topological phase

Different from the spin-1 Haldane gapped phase, we propose a novel SO(3) spin-1 matrix product state (MPS), whose parent Hamiltonian includes three-site spin interactions. From the entanglement spectrum of a single block with $l$ sites, an enlarged SU(3) symmetry is identified in the edge states, which are conjugate to each other for the $l=even$ block but identical for the $l=odd$ block. By blocking this novel state, the blocked MPS explicitly displays the SU(3) symmetry with two distinct structures. Under a symmetric bulk bipartition with a sufficient large block length $% l=even$, the entanglement Hamiltonian (EH) of the reduced system characterizes a spontaneous dimerized phase with two-fold degeneracy. However, for the block length $l=odd$, the corresponding EH represents an SU(3) quantum critical point with delocalized edge quasiparticles, and the critical field theory is described by the SU(3) level-1 Wess-Zumino-Witten conformal field theory.

cond-mat.str-el↗

arXiv2014

Critical entanglement spectrum of one-dimensional symmetry protected topological phases

Under an appropriate symmetric extensive bipartition in a one-dimensional symmetry protected topological (SPT) phase, a bulk critical entanglement spectrum can be obtained, resembling the excitation spectrum of the critical point separating the SPT phase from the trivial (vacuum) state. Such a critical point is beyond the standard Landau-Ginzburg-Wilson paradigm for symmetry breaking phase transitions. For the $S=1$ SPT (Haldane) phase with the Affleck-Kennedy-Lieb-Tasaki exact wave function, the resulting critical entanglement spectrum has a residual entropy per lattice site $s_{r}=0.67602$, showing a delocalized version of the edge excitations in the SPT phase. From the wave function corresponding to the lowest entanglement energy level, the central charge of the critical point can be extracted $c\approx 1.01\pm 0.01$. The critical theory can be identified as the same effective field theory as the spin-1/2 antiferromagnetic Heisenberg chain or the spin-1/2 Haldane-Shastry model with inverse square long-range interaction.

cond-mat.str-el↗

arXiv2014

Disentangling topological degeneracy in the entanglement spectrum of one-dimensional symmetry protected topological phases

One-dimensional valence bond solid (VBS) states represent the simplest symmetry protected topological phases. We show that their ground state entanglement spectrum contains both topological and non-topological structures. For the $SO(3)$ symmetric VBS states with odd-integer spins, the two-fold topological degeneracy is associated with an underlying $Z_{2}\times Z_{2}$ symmetry that protects the corresponding topological phase. In general, for the $SO(2S+1)$ symmetric VBS states with integer spins $S$, the corresponding protecting symmetry is identified as the $(Z_{2}\times Z_{2})^{S}$ symmetry, yielding the $2^{S}$-fold topological degeneracy. The topological degeneracy and associated protecting symmetry can be identified by a non-local unitary transformation, which changes the topological order of the VBS states into conventional ferromagnetic order.

cond-mat.str-el↗