arXiv subjects

Shijie Hu

Publications and source records attributed to Shijie Hu.

At least 19 recordsLinked to original sources

arXiv2026

Crossover and Changeover in Spin-1 Kitaev-$\Gamma$ Chain with Uniaxial Single-ion Anisotropy

Recent advances in bond-directional spin chains have revealed extensive emergent phenomena and unconventional criticality. Here we investigate the spin-1 Kitaev-$\Gamma$ chain with uniaxial single-ion anisotropy (SIA) using large-scale density-matrix renormalization group calculations and bosonization analysis. Tuning the SIA strength reveals a crossover from the Kitaev phase to the large-$D$ phase, evidenced by the excitation gap changing from quadratic to linear, the coexistence and smooth evolution of spin-nematic and string order parameters, and the suppression of the double-peak specific heat. For negative SIA, we uncover a changeover from a first-order transition to a continuous one between the dimerized and Haldane phases. The continuous transition belongs to the \textrm{SU(2)$_2$} Wess-Zumino-Witten universality class with central charge $c=3/2$, a rare instance in a system without continuous symmetry. Our results establish the Kitaev-$\Gamma$ chain as a minimal platform for controlling crossover and changeover phenomena.

cond-mat.str-el↗

arXiv2026

Encoding complex-balanced thermalization in quantum circuits

Non-Markovian dynamics in open quantum systems often invalidates the complex-balanced thermalization framework, hindering predictive control of quantum simulation platforms designed to prepare out-of-equilibrium states at prescribed temperatures. We resolve this bottleneck by engineering reservoir qubits as modular microscopic units coupled to a target quantum system and constructing a quantum-circuit platform that enforces strictly Markovian complex-balanced thermalization. The platform exploits the non-orthogonality of reservoir qubit eigenstates to drive inhomogeneous heating through a modified Kubo-Martin-Schwinger relation, and uses tunable microscopic time-reversibility breaking to generate amplification-dissipation dynamics. We demonstrate two applications: temporally correlated dichromatic emission and Liouvillian exceptional-point-protected quantum synchronization at finite temperatures, displaying predictive control over out-of-equilibrium state preparation.

quant-ph↗

arXiv2025

Altermagnetism and beyond in the $t$-$t^\prime$-$\delta$ Fermi-Hubbard model

In this work, we revisit the phase diagram of the $t$-$t^\prime$-$\delta$ Fermi-Hubbard model on the square lattice to gain a more comprehensive understanding of this correlated model at half filling. This model has recently become a prominent topic of research because it hosts altermagnetic phases. Using mean-field analysis, we identify four metallic phases and two insulating phases with nontrivial magnetic orders at an intermediate value of $\delta = 0.5$, presenting a rich ground-state phase diagram in the $U$-$t^\prime$ plane. We also highlight the distinct features of the Fermi surface topology for each metallic phase. To go beyond the mean-field theory, we employ the density-matrix renormalization group method to simulate the ground state numerically. The phase boundaries are determined from the discontinuities and peaks in the entanglement entropy and magnetizations. In addition to the phases identified in the mean-field theory, we find a valence-bond solid state in a narrow intermediate-$t'$ region. Our work offers a firm step forward in understanding the complex behaviors of correlated electrons in the $t$-$t^\prime$-$\delta$ Hubbard model over a large parameter space.

cond-mat.str-el↗

arXiv2024

Anyonic phase transitions in the 1D extended Hubbard model with fractional statistics

We study one-dimensional (1D) lattice anyons with extended Hubbard interactions at unit filling using bosonization and numerical simulations. The behavior can be continuously tuned from Bosonic to Fermionic behavior by adjusting the topological exchange angle $\theta$, which leads to a competition of different instabilities. We present the bosonization theory in presence of dynamic gauge fields, which predicts a phase diagrams of four different gapped phases with distinct dominant correlations. Advanced numerical simulations determine and analyze the exact phase transitions between Mott insulator, charge density wave, dimerized state, and Haldane insulator, all of which meet at a multi-critical line in the parameter space of anyonic angle $\theta$, onsite interaction $U$, and nearest neighbor repulsion $V$. Superfluid and pair-superfluid phases are stable in a region of small $V$.

cond-mat.str-el↗

arXiv2024

Realization of a period-3 coplanar state in one-dimensional spin-orbit coupled optical lattice

In ultracold atoms, achieving a period-$3$ structure poses a significant challenge. In this work, we propose a three-sublattice spin-flop transition mechanism, differing from the two-sublattice counterpart used to explain the emergence of ferrimagnetic orders in higher dimensions. Guided by this mechanism, we design a setup of alkaline-earth-metal atoms to create a spin-orbit coupled optical lattice, where we identify a triplet-fold degenerate $YX\bar{Y}$ state with a period-$3$ coplanar spin ordering within the deep Mott-insulating phase region of the ground-state phase diagram. The $YX\bar{Y}$ state is protected by a finite gap, and its characteristic angle can be finely tuned by specific setup parameters. Moreover, we use the Rabi spectroscopy technique to detect the $YX\bar{Y}$ state. Our work not only shows the feasibility of achieving a period-$3$ structure \textit{via} the new mechanism but also suggests its potential applications for exploring other periodic structures in optical lattices.

cond-mat.quant-gas↗

arXiv2024

Diagnosing thermalization dynamics of non-Hermitian quantum systems via GKSL master equations

The application of the eigenstate thermalization hypothesis to non-Hermitian quantum systems has become one of the most important topics in dissipative quantum chaos, recently giving rise to intense debates. The process of thermalization is intricate, involving many time-evolution trajectories in the reduced Hilbert space of the system. By considering two different expansion forms of the density matrices adopted in the biorthogonal and right-state time evolutions, we have derived two versions of the Gorini-Kossakowski-Sudarshan-Lindblad master equations describing the non-Hermitian systems coupled to a bosonic heat bath in thermal equilibrium. By solving the equations, we have identified a sufficient condition for thermalization under both time evolutions, resulting in Boltzmann biorthogonal and right-eigenstate statistics, respectively. This finding implies that the recently proposed biorthogonal random matrix theory needs an appropriate revision. Moreover, we have exemplified the precise dynamics of thermalization and thermodynamic properties with test models.

quant-ph↗

arXiv2024

Density-matrix renormalization group algorithm for non-Hermitian systems

A biorthonormal-block density-matrix renormalization group algorithm is proposed to accurately compute properties of large-scale non-Hermitian many-body systems, in which a renormalized-space partition of the non-Hermitian reduced density matrix is implemented to fulfill the prerequisite for the biorthonormality of the renormalization group (RG) transformation and to optimize the construction of saved Hilbert spaces. A redundancy in saved spaces of the reduced density matrix is exploited to reduce a condition number resulting from the non-unitarity of the left and right transformation matrices, in order to ensure the numerical stability of the RG procedure. The algorithm is successfully applied to an interacting fermionic Su-Schrieffer-Heeger model with nonreciprocal hoppings and staggered complex chemical potential, exhibiting novel many-body phenomena.

cond-mat.str-el↗

arXiv2023

Principle of learning sign rules by neural networks in qubit lattice models

A neural network is a powerful tool that can uncover hidden laws beyond human intuition. However, it often appears as a black box due to its complicated nonlinear structures. By drawing upon the Gutzwiller mean-field theory, we can showcase a principle of sign rules for ordered states in qubit lattice models. We introduce a shallow feed-forward neural network with a single hidden neuron to present these sign rules. We conduct systematical benchmarks in various models, including the generalized Ising, spin-$1/2$ XY, (frustrated) Heisenberg rings, triangular XY antiferromagnet on a torus, and the Fermi-Hubbard ring at an arbitrary filling. These benchmarks show that all the leading-order sign rule characteristics can be visualized in classical forms, such as pitch angles. Besides, quantum fluctuations can result in an imperfect accuracy rate quantitatively.

cond-mat.str-el↗

arXiv2023

Nonuniform quadrupolar orders in the spin-3/2 generalized Heisenberg chain

The generation of nonuniform quadrupole states plays a crucial role in understanding various fascinating phenomena observed in the advancement of several research areas, e.g., multiferroic compounds, nonmagnetic superconductors, etc. In this work, we investigate the ground-state phase diagram of a generalized spin-3/2 bilinear-biquadratic-bicubic Heisenberg chain in the representation of multipolar operators. By numerical simulations with the large-scale density-matrix renormalization group (DMRG) method, we successfully identify a tetramerization phase and a stripe-Q phase. These phases are characterized by the emergence of nonuniform quadrupole orders resulting from the spontaneous breaking of translation symmetry. In particular, tetramerization phase refers to the quadrupole operators take a four-cycle, while the stripe-Q phase represents a striped pattern in quadrupole operators. Additionally, we demonstrate the presence of a Wess-Zumino-Witten (WZW) model with level k = 1 at the transition point between the dimerized (DM) phase and the Luttinger liquid (LL) phase, based on strong numerical findings.

cond-mat.str-el↗

arXiv2023

Phase transitions in the Haldane-Hubbard model

The Haldane-Hubbard model is a prime example of the combined effects of band topology and electronic interaction. We revisit its spinful phase diagram at half-filling as a consensus on the presence of SU($2$) symmetry is currently lacking. To start, we utilize the Hartree-Fock mean-field method, which offers a direct understanding of symmetry breaking through the effective mass term that can acquire spin dependence. Our results, in agreement with previous studies, provide an instructive insight into the regime where the Chern number $C=1$, with only one spin species remaining topological. Besides that, we numerically study the phase diagram of the Haldane-Hubbard model via a large-scale infinite-density matrix renormalization group (iDMRG) method. The phase boundaries are determined by the Chern number and the correlation lengths obtained from the transfer-matrix spectrum. Unlike previous studies, the iDMRG method investigates the Haldane-Hubbard model on a thin and infinitely long cylinder and examines scenarios consistent with the two-dimensional thermodynamic limit. Here, the phase diagram we obtained qualitatively goes beyond the Hartree-Fock scope, particularly in the $C=1$ region, and serves as a quantitative benchmark for further theoretical and experimental investigations.

cond-mat.str-el↗

arXiv2023

Sampling reduced density matrix to extract fine levels of entanglement spectrum and restore entanglement Hamiltonian

The reduced density matrix (RDM) plays a key role in quantum entanglement and measurement, as it allows the extraction of almost all physical quantities related to the reduced degrees of freedom. However, restricted by the degrees of freedom in the environment, the total system size is often limited, let alone the subsystem. To address this challenge, we propose a quantum Monte Carlo scheme with a low technical barrier, enabling precise extraction of the RDM. To demonstrate the power of the method, we present the fine levels of the entanglement spectrum (ES), which is the logarithmic eigenvalues of the RDM. We clearly show the ES for a $1$D ladder with a long entangled boundary, and that for the $2$D Heisenberg model with a tower of states. Furthermore, we put forward an efficient way to restore the entanglement Hamiltonian in operator-form from the sampled RDM data. Our simulation results, utilizing unprecedentedly large system sizes, establish a practical computational framework for determining entanglement quantities based on the RDM, such as the ES, particularly in scenarios where the environment has a huge number of degrees of freedom.

quant-ph↗

arXiv2023

Spontaneous dimerization, spin-nematic order, and deconfined quantum critical point in a spin-1 Kitaev chain with tunable single-ion anisotropy

The Kitaev-type spin chains have been demonstrated to be fertile playgrounds in which exotic phases and unconventional phase transitions are ready to appear. In this work, we use the density-matrix renormalization group method to study the quantum phase diagram of a spin-1 Kitaev chain with a tunable negative single-ion anisotropy (SIA). When the strength of the SIA is small, the ground state is revealed to be a spin-nematic phase which escapes conventional magnetic order but is characterized by a finite spin-nematic correlation because of the breaking spin-rotational symmetry. As the SIA increases, the spin-nematic phase is taken over by either a dimerized phase or an antiferromagnetic phase through an Ising-type phase transition, depending on the direction of the easy axis. For large enough SIA, the dimerized phase and the antiferromagnetic phase undergo a ``Landau-forbidden" continuous phase transition, suggesting new platform of deconfined quantum critical point in spin-1 Kitaev chain.

cond-mat.str-el↗

arXiv2023

Charge Stripe Manipulation of Superconducting Pairing Symmetry Transition

Charge stripes have been widely observed in many different types of unconventional superconductors, holding varying periods ($\mathcal{P}$) and intensities. However, a general understanding on the interplay between charge stripes and superconducting properties is still incomplete. Here, using large-scale unbiased numerical simulations on a general inhomogeneous Hubbard model, we discover that the charge-stripe period $\mathcal{P}$, which is variable in different real material systems, could dictate the pairing symmetries -- $d$ wave for $\mathcal{P} \ge 4$, $s$ and $d$ waves for $\mathcal{P} \le 3$. In the latter, tuning hole doping and charge-stripe amplitude can trigger a $d$-$s$ wave transition and magnetic-correlation shift, where the $d$-wave state converts to a pairing-density wave state, competing with the $s$ wave. These interesting phenomena arise from an unusual stripe-induced selection rule of pairing symmetries around on-stripe region and within inter-stripe region, giving rise to a critical point of $\mathcal{P}=3$ for the phase transition. In general, our findings offer new insights into the differences in the superconducting pairing mechanisms across many $\mathcal{P}$-dependent superconducting systems, highlighting the decisive role of charge stripe.

cond-mat.str-el↗

arXiv2023

Negative superinflating bipartite fluctuations near exceptional points in $\mathcal{PT}$-symmetric models

We investigate bipartite particle number fluctuations near the rank-$2$ exceptional points (EPs) of $\mathcal{PT}$-symmetric Su-Schrieffer-Heeger models. Beyond a conformal field theory of massless fermions, fluctuations or equivalently compressibility is negative definite and exhibits superinflation in leading order at EPs, due to the defectiveness in the biorthogonal Hilbert space. Associated with the bipartite von Neumann entanglement entropy, a parameter in an anomalous correspondence referencing from a purely non-Hermitian limit helps characterize two inequivalent EP sets. Our work paves the way for understanding the singularity of fluctuations relevant to EPs, more promisingly detectable in experiments.

cond-mat.mes-hall↗

arXiv2022

Quantum phase diagram for two species hardcore bosons in one-dimensional optical lattices with the resonantly driven Rabi frequency

We propose an experimental realization of the time-periodically modulated Rabi frequency and suggest density-dependent hoppings of two species hardcore bosons in a one-dimensional optical lattice. Distinct from the previous work [Phys. Rev. Research {\bf 2}, 013275 (2020)], we study effects in the first resonance region. In the effective Hamiltonian, the intra-species hopping occurs only if the density discrepancy of the other species on these sites is zero, while the inter-species one is allowed once the relevant density discrepancy becomes nonzero. At integer-$1$ filling, the quantum phase diagram of the effective Hamiltonian is determined by the perturbation analysis together with numerical calculations. We find that in the limit of dominant $J_{1}$, the system becomes a double-degenerate dimerized state, with spontaneously breaking the translation symmetry. The interplay of $J_{0}$, $J_{1}$ and the fixed ${\bar U}=1$ leads to three BKT transition lines and a tricritical BKT point. Exact transition lines are obtained by the level spectroscopic technique. Besides, general physical properties, including the charge gap, neutral gap, superfluid density and dimerization strength, are investigated as well.

cond-mat.quant-gas↗

arXiv2021

Interplay of interactions, disorder and topology in the Haldane-Hubbard model

We investigate the ground-state phase diagram of the spinless Haldane-Hubbard model in the presence of quenched disorder, contrasting results obtained from both exact diagonalization as well as density matrix renormalization group, applied to a honeycomb cylinder. The interplay of disorder, interactions and topology gives rise to a rich phase diagram, and in particular highlights the possibility of a disorder-driven trivial-to-topological transition in the presence of finite interactions. That is, the topological Anderson insulator, demonstrated in non-interacting settings, is shown to be stable to the presence of sufficiently small interactions before a charge density wave Mott insulator sets in. We further perform a finite-size analysis of the transition to the ordered state in the presence of disorder, finding a mixed character of first and second order transitions in finite lattices, tied to specific conditions of disorder realizations and boundary conditions used.

cond-mat.str-el↗

arXiv2021

Unusual excitations and double-peak specific heat in a bond-alternating spin-$1$ $K$-$Γ$ chain

One-dimensional gapped phases that avoid any symmetry breaking have drawn enduring attention. In this paper, we study such phases in a bond-alternating spin-1 $K$-$Γ$ chain built of a Kitaev ($K$) interaction and an off-diagonal $Γ$ term. In the case of isotropic bond strength, a Haldane phase, which resembles the ground state of a spin-$1$ Heisenberg chain, is identified in a wide region. A gapped Kitaev phase situated at dominant ferromagnetic and antiferromagnetic Kitaev limits is also found. The Kitaev phase has extremely short-range spin correlations and is characterized by finite $\mathbb{Z}_2$-valued quantities on bonds. Its lowest entanglement spectrum is unique, in contrast to the Haldane phase whose entanglement spectrum is doubly degenerate. In addition, the Kitaev phase shows a double-peak structure in the specific heat at two different temperatures. In the pure Kitaev limit, the two peaks are representative of the development of short-range spin correlation at $T_h \simeq 0.5680$ and the freezing of $\mathbb{Z}_2$ quantities at $T_l \simeq 0.0562$, respectively. By considering bond anisotropy, regions of Haldane phase and Kitaev phase are enlarged, accompanied by the emergence of dimerized phases and three distinct magnetically ordered states.

cond-mat.str-el↗

arXiv2021

Interplay of local order and topology in the extended Haldane-Hubbard model

We investigate the ground-state phase diagram of the spinful extended Haldane-Hubbard model on the honeycomb lattice using an exact-diagonalization, mean-field variational approach, and further complement it with the infinite density matrix renormalization group, applied to an infinite honeycomb cylinder. This model, governed by both on-site and nearest-neighbor interactions, can result in two types of insulators with finite local order parameters, either with spin or charge ordering. Moreover, a third one, a topologically nontrivial insulator with nonlocal order, is also manifest. We test expectations of previous analyses in spinless versions asserting that once a local order parameter is formed, the topological characteristics of the ground state, associated with a finite Chern number, are no longer present, resulting in a topologically trivial wave function. Our study confirms this overall picture, and highlights how finite-size effects may result in misleading conclusions on the coexistence of finite local order parameters and nontrivial topology in this model.

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