Searcharxiv⌕ Search

arXiv subjects

Shi-Jian Gu

Publications and source records attributed to Shi-Jian Gu.

At least 19 recordsLinked to original sources
arXiv2016

The scaling behavior of logarithmic fidelity in quantum phase transition in LMG model

In this paper, we explore the differences between classical logarithmic fidelity and quantum fidelity. The classical logarithmic fidelity is found to be always extensive while the quantum one manifests distinct size dependence in different phases. Illustrated by the anisotropic Lipkin-Meshkov-Glick model, we found numerically and analytically that the logarithmic fidelity scales like N in the symmetry-broken phase and scales like N^0 in the polarized phase. The singular behavior around the critical point is also investigated.

cond-mat.stat-mech↗
arXiv2014

Ground state properties of a Tonks-Girardeau Gas in a periodic potential

In this paper, we investigate the ground-state properties of a bosonic Tonks-Girardeau gas confined in a one-dimensional periodic potential. The single-particle reduced density matrix is computed numerically for systems up to $N=265$ bosons. Scaling analysis of the occupation number of the lowest orbital shows that there are no Bose-Einstein Condensation(BEC) for the periodically trapped TG gas in both commensurate and incommensurate cases. We find that, in the commensurate case, the scaling exponents of the occupation number of the lowest orbital, the amplitude of the lowest orbital and the zero-momentum peak height with the particle numbers are 0, -0.5 and 1, respectively, while in the incommensurate case, they are 0.5, -0.5 and 1.5, respectively. These exponents are related to each other in a universal relation.

cond-mat.stat-mech↗
arXiv2014

Fidelity susceptibilities in the one-dimensional extended Hubbard model

We investigated the fidelity susceptibility in the one-dimension (1D) Hubbard model and the extended Hubbard model at half-filling via the density matrix renormalization group. From the numerical results, we argue that in the 1D Hubbard model, the fidelity susceptibility shows a divergence at two points which is infinitesimally close to the critical point while it is always extensive exactly at the critical point. For the extended Hubbard model, we found that for a properly chosen driving parameter, the fidelity susceptibility is able to reveal the quantum phase transitions between the PS (phase separation)-superconducting, superconducting-CDW (charge-density wave), CDW-SDW(spin-density wave), SDW-PS, CDW-BOW (bond-order wave), and the BOW-SDW phases.

cond-mat.str-el↗
arXiv2014

Density Matrix Spectra and Order Parameters in the 1D Extended Hubbard Model

Without any knowledge of the symmetry existing in the system, we derive the exact forms of the order parameters which show long-range correlation in the ground state of the one-dimensional extended Hubbard model using a quantum information approach. Our work demonstrates that the quantum information approach can help us to find the explicit form of the order parameter, which cannot be derived systematically via traditional methods in the condensed matter theory.

cond-mat.str-el↗
arXiv2014

Spectral function and fidelity susceptibility in quantum critical phenomena

In this paper, we derive a simple equality that relates the spectral function $I(k,ω)$ and the fidelity susceptibility $χ_F$, i.e. $% χ_F=\lim_{η\rightarrow 0}\fracπη I(0, iη)$ with $η$ being the half-width of the resonance peak in the spectral function. Since the spectral function can be measured in experiments by the neutron scattering or the angle-resolved photoemission spectroscopy(ARPES) technique, our equality makes the fidelity susceptibility directly measurable in experiments. Physically, our equality reveals also that the resonance peak in the spectral function actually denotes a quantum criticality-like point at which the solid state seemly undergoes a significant change.

cond-mat.str-el↗
arXiv2013

The Euler Number of Bloch States Manifold and the Quantum Phases in Gapped Fermionic Systems

We propose a topological Euler number to characterize nontrivial topological phases of gapped fermionic systems, which originates from the Gauss-Bonnet theorem on the Riemannian structure of Bloch states established by the real part of the quantum geometric tensor in momentum space. Meanwhile, the imaginary part of the geometric tensor corresponds to the Berry curvature which leads to the Chern number characterization. We discuss the topological numbers induced by the geometric tensor analytically in a general two-band model. As an example, we show that the zero-temperature phase diagram of a transverse field XY spin chain can be distinguished by the Euler characteristic number of the Bloch states manifold in a (1+1)-dimensional Bloch momentum space.

cond-mat.str-el↗
arXiv2013

Absence of finite-temperature ballistic charge transport in the 1D half-filled Hubbard model

Finite-temperature T>0 transport properties of integrable and nonintegrable one-dimensional (1D) many-particle quantum systems are rather different, showing in the metallic phases ballistic and diffusive behavior, respectively. The repulsive 1D Hubbard model is an integrable system of wide physical interest. For electronic densities $n\neq1$ it is an ideal conductor, with ballistic charge transport for T larger or equal to 0. In spite that it is solvable by the Bethe ansatz, at $n=1$ its T>0 transport properties are a collective-behavior issue that remains poorly understood. Here we combine that solution with symmetry to show that for on-site repulsion U>0 the charge stiffness D (T) vanishes for T>0 in the thermodynamic limit. This absence of finite-temperature ballistic charge transport is an exact result that clarifies a long-standing open problem.

cond-mat.str-el↗
arXiv2012

Construct order parameter from the spectra of mutual information

In this paper, we try to establish a connection between a quantum information concept, i.e. the mutual information, and the conventional order parameter in condensed matter physics. We show that a non-vanishing mutual information at a long distance means the existence of long-range order. By analyzing the entanglement spectra of the reduced density matrix that are used to calculate the mutual information, we show how to find the local order operator used to identify various phases with long-rang order.

quant-ph↗
arXiv2011

Bell Function Values Approach to Topological Quantum Phase Transitions

We investigate the relation between Bell function values (BFV) of the reduced density matrix and the topological quantum phase transitions in the Kitaev-Castelnovo-Chamon model. % [Phys. Rev. B \textbf{77}, %054433 (2008)]. We find that the first order derivative of BFV exhibits singular behavior at the critical point and we propose that it can serve as a good and convenient marker for the transition point. More interestingly, the value of the critical point can be analytically obtained in this approach. Since the BFV serves as a measure of nonlocality when it is greater than the classical bound of the correlation functions, our work has established a link between quantum nonlocality and phase transitions.

quant-ph↗
arXiv2011

A spin chain with spiral orders: perspectives of quantum information and mechanical response

In this paper, we study the ground state of a one-dimensional exactly solvable model with a spiral order. While the model's energy spectra is the same as the one-dimensional transverse field Ising model, its ground state manifests spiral order with various periods. The quantum phase transition from a spiral-order phase to a paramagnetic phase is investigated in perspectives of quantum information science and mechanics. We show that the modes of the ground-state fidelity and its susceptibility can tell the change of periodicity around the critical point. We study also the spin torsion modulus which defines the coefficient of the potential energy stored under a small rotation. We find that at the critical point, it is a constant; while away from the critical point, the spin torsion modulus tends to zero.

cond-mat.str-el↗
arXiv2011

Scaling of quantum Zeno dynamics in thermodynamic systems

We study the quantum Zeno effect (QZE) in two many-body systems, namely the one-dimensional transverse-field Ising model and the Lipkin-Meshkov-Glick (LMG) model, coupled to a central qubit. Our result shows that in order to observe QZE in the Ising model, the frequency of the projective measurement should be of comparable order to that of the system sizes. The same criterion also holds in the symmetry broken phase of the LMG model while in the model's polarized phase, the QZE can be easily observed.

cond-mat.str-el↗
arXiv2010

Mixture of Tonks-Girardeau gas and Fermi gas in one-dimensional optical lattices

We study the Bose-Fermi mixture with infinitely boson-boson repulsion and finite boson-Fermion repulsion. By using a generalized Jordan-Wigner transformation, we show that the system can be mapped to a repulsive Hubbard model and thus can be solved exactly for the case with equal boson and fermion masses. By using the Bethe-ansatz solutions, we investigate the ground state properties of the mixture system. Our results indicate that the system with commensurate filling $n=1$ is a charge insulator but still a superfluid with non-vanishing superfluid density. We also briefly discuss the case with unequal masses for bosons and fermions.

cond-mat.quant-gas↗
arXiv2010

Reduced fidelity in Kitaev honeycomb model

We study the reduced fidelity and reduced fidelity susceptibility in the Kitaev honeycomb model. It is shown that the reduced fidelity susceptibility of two nearest site manifest itself a peak at the quantum phase transition point, although the one-site reduced fidelity susceptibility vanishes. Our results directly reveal that the reduced fidelity susceptibility can be used to characterize the quantum phase transition in the Kitaev honeycomb model, and thus suggest that the reduced fidelity susceptibility is an accurate marker of the topological phase transition when it is properly chosen, despite of its local nature.

cond-mat.str-el↗
arXiv2009

Repeater-assisted Zeno effect in classical stochastic processes

As a classical state, for instance a digitized image, is transferred through a classical channel, it decays inevitably with the distance due to the surroundings' interferences. However, if there are enough number of repeaters, which can both check and recover the state's information continuously, the state's decay rate will be significantly suppressed, then a classical Zeno effect might occur. Such a physical process is purely classical and without any interferences of living beings, therefore, it manifests that the Zeno effect is no longer a patent of quantum mechanics, but does exist in classical stochastic processes.

physics.data-an↗
arXiv2009

Entropy majorization, thermal adiabatic theorem, and quantum phase transitions

Let a general quantum many-body system at a low temperature adiabatically cross through the vicinity of the system's quantum critical point. We show that the system's temperature is significantly suppressed due to both the entropy majorization theorem in quantum information science and the entropy conservation law in adiabatic processes. We take the one-dimensional transverse-field Ising model and spinless fermion system as concrete examples to show that the inverse temperature might become divergent around their critical points. Since the temperature is a measurable quantity in experiments, our work, therefore, provides a practicable proposal to detect quantum phase transitions.

cond-mat.stat-mech↗
arXiv2009

Fidelity susceptibility in the two-dimensional transverse field Ising and XXZ models

We study the fidelity susceptibility in the two-dimensional(2D) transverse field Ising model and the 2D XXZ model numerically. It is found that in both models, the fidelity susceptibility as a function of the driving parameter diverges at the critical points. The validity of the fidelity susceptibility to signal for the quantum phase transition is thus verified in these two models. We also compare the scaling behavior of the extremum of the fidelity susceptibility to that of the second derivative of the ground state energy. From those results, the theoretical argument that fidelity susceptibility is a more sensitive seeker for a second order quantum phase transition is also testified in the two models.

cond-mat.stat-mech↗
arXiv2009

Exact solutions of a one-dimensional mixture of spinor bosons and spinor fermions

The exact solutions of a one-dimensional mixture of spinor bosons and spinor fermions with $δ$-function interactions are studied. Some new sets of Bethe ansatz equations are obtained by using the graded nest quantum inverse scattering method. Many interesting features appear in the system. For example, the wave function has the $SU(2|2)$ supersymmetry. It is also found that the ground state of the system is partial polarized, where the fermions form a spin singlet state and the bosons are totally polarized. From the solution of Bethe ansatz equations, it is shown that all the momentum, spin and isospin rapidities at the ground state are real if the interactions between the particles are repulsive; while the fermions form two-particle bounded states and the bosons form one large bound state, which means the bosons condensed at the zero momentum point, if the interactions are attractive. The charge, spin and isospin excitations are discussed in detail. The thermodynamic Bethe ansatz equations are also derived and their solutions at some special cases are obtained analytically.

cond-mat.str-el↗