arXiv subjects

Gao Xianlong

Publications and source records attributed to Gao Xianlong.

At least 91 records · Page 5Linked to original sources

arXiv2017

Dynamical signature of localization-delocalization transition in one-dimensional incommensurate lattice

We investigate the quench dynamics of a one-dimensional incommensurate lattice described by the Aubry-André model by a sudden change of the strength of incommensurate potential $Δ$ and unveil that the dynamical signature of localization-delocalization transition can be characterized by the occurrence of zero points in the Loschmit echo. For the quench process with quenching taking place between two limits of $Δ=0$ and $Δ=\infty$, we give analytical expressions of the Loschmidt echo, which indicate the existence of a series of zero points in the Loschmidt echo. For a general quench process, we calculate the Loschmidt echo numerically and analyze its statistical behavior. Our results show that if both the initial and post-quench Hamiltonian are in extended phase or localized phase, Loschmidt echo will always be greater than a positive number; however if they locate in different phases, Loschmidt echo can reach nearby zero at some time intervals.

cond-mat.dis-nn↗

arXiv2016

Phase diagram of the off-diagonal Aubry-André model

We study a one-dimensional quasiperiodic system described by the off-diagonal Aubry-André model and investigate its phase diagram by using the symmetry and the multifractal analysis. It was shown in a recent work ({\it Phys. Rev. B} {\bf 93}, 205441 (2016)) that its phase diagram was divided into three regions, dubbed the extended, the topologically-nontrivial localized and the topologically-trivial localized phases, respectively. Out of our expectation, we find an additional region of the extended phase which can be mapped into the original one by a symmetry transformation. More unexpectedly, in both "localized" phases, most of the eigenfunctions are neither localized nor extended. Instead, they display critical features, that is, the minimum of the singularity spectrum is in a range $0<γ_{min}<1$ instead of $0$ for the localized state or $1$ for the extended state. Thus, a mixed phase is found with a mixture of localized and critical eigenfunctions.

cond-mat.dis-nn↗

arXiv2016

Dynamical properties of the Rabi model

We study the dynamical properties of the quantum Rabi model within a systematic expansion method. Based on the observation that the parity symmetry of the Rabi model is kept during the evolution of the states, we decompose the initial state and the time-dependent one into a part of a positive and a negative parity expanded by the superposition of the coherent states. The evolutions for the corresponding positive and the negative parity are obtained, where the expansion coefficients in the dynamical equations are known from the recurrence relation derived.

quant-ph↗

arXiv2016

Almost mobility edges and existence of critical regions in one-dimensional quasiperiodic lattices

We study a one-dimensional quasiperiodic system described by the Aubry-André model in the small wave vector limit and demonstrate the existence of almost mobility edges and critical regions in the system. It is well known that the eigenstates of the Aubry-André model are either extended or localized depending on the strength of incommensurate potential $V$ being less or bigger than a critical value $V_c$, and thus no mobility edge exists. However, it was shown in a recent work that this conclusion does not hold true when the wave vector $α$ of the incommensurate potential is small, and for the system with $V V_c$, for which all eigenstates are localized states, but can be divided into extended, critical and localized states in their dual space by utilizing the self-duality property of the Aubry-André model.

cond-mat.dis-nn↗

arXiv2016

Rederivation of the Casimir force under the completeness relation of continuum operator

Casimir effects manifests that, the two closely paralleled plates, generally produce a macroscopic attractive force due to the quantum vacuum fluctuations of the electromagnetic fields. The derivation of the force requires an {\it artificial} regulator by removing the divergent summation. By including naturally a spectrum density factor, based on the observation that an incomplete eigenvectors of observable, such as the eigenstates for the photons in the free field, can form a complete set of eigenvectors by introducing a unique spectrum transformation, an alternative way is presented to rederive the force, without using a regulator. As a result, the Casimir forces are obtained with the first term $-π^2 \hbar c/(240 a^4)$ attractive, and the second one, $-π^4 \hbar c^3 σ^2/(1008 a^6)$, also attractive but smaller, with $a$ the plate separation, and $σ$ a to-be-determined small constant number in the spectrum density factor.

hep-th↗

arXiv2015

Anderson localization of Cooper pairs and Majorana fermions in an ultracold atomic Fermi gas with synthetic spin-orbit coupling

We theoretically investigate two-particle and many-particle Anderson localizations of a spin-orbit coupled ultracold atomic Fermi gas trapped in a quasi-periodic potential and subjected to an out-of-plane Zeeman field. We solve exactly the two-particle problem in a finite length system by exact diagonalization and solve approximately the many-particle problem within the mean-field Bogoliubov-de Gennes approach. At a small Zeeman field, the localization properties of the system are similar to that of a Fermi gas with conventional $s$-wave interactions. As the disorder strength increases, the two-particle binding energy increases and the fermionic superfluidity of many particles disappears above a threshold. At a large Zeeman field, where the interatomic interaction behaves effectively like a $p$-wave interaction, the binding energy decreases with increasing disorder strength and the resulting topological superfluidity shows a much more robust stability against disorder than the conventional $s$-wave superfluidity. We also analyze the localization properties of the emergent Majorana fermions in the topological phase. Our results could be experimentally examined in future cold-atom experiments, where the spin-orbit coupling can be induced artificially by using two Raman lasers, and the quasi-periodic potential can be created by using bichromatic optical lattices.

cond-mat.quant-gas↗

arXiv2015

Phase diagram of a non-Abelian Aubry-André-Harper model with $p$-wave superfluidity

We theoretically study a one-dimensional quasi-periodic Fermi system with topological $p$-wave superfluidity, which can be deduced from a topologically non-trivial tight-binding model on the square lattice in a uniform magnetic field and subject to a non-Abelian gauge field. The system may be regarded a non-Abelian generalization of the well-known Aubry-André-Harper model. We investigate its phase diagram as functions of the strength of the quasi-disorder and the amplitude of the $p$-wave order parameter, through a number of numerical investigations, including a multifractal analysis. There are four distinct phases separated by three critical lines, i.e., two phases with all extended wave-functions (I and IV), a topologically trivial phase (II) with all localized wave-functions and a critical phase (III) with all multifractal wave-functions. The phase I is related to the phase IV by duality. It also seems to be related to the phase II by duality. Our proposed phase diagram may be observable in current cold-atom experiments, in view of simulating non-Abelian gauge fields and topological insulators/superfluids with ultracold atoms.

cond-mat.quant-gas↗

arXiv2014

Three-component topological superfluid in one-dimensional Fermi gases with spin-orbit coupling

We theoretically investigate one-dimensional three-component spin-orbit-coupled Fermi gases in the presence of Zeeman field. By solving the Bogoliubov-de-Gennes equations, we obtain the phase diagram at given chemical potential and order parameter. We show that the system undergoes a phase transition from Bardeen-Cooper-Schrieffer superfluid to topological superfluid as increasing the intensity of Zeeman field. By comparing to the two-component system, we find, besides the topological phase transition from the trivial superfluid to nontrivial topological superfluid, the system can always be in a nontrivial topological superfluid, and there are two Majorana zero energy regions while increasing the magnetic field. We find the three-component spin-orbit-coupled Fermi gases in certain parameter range is more optimizing for experimental realization due to the smaller magnetic field needed. We therefore propose a promising candidate for realizing topological superfluid.

cond-mat.quant-gas↗

arXiv2014

Topological phase transition in the quench dynamics of a one-dimensional Fermi gas

We study the quench dynamics of a one-dimensional ultracold Fermi gas in an optical lattice potential with synthetic spin-orbit coupling. At equilibrium, the ground state of the system can undergo a topological phase transition and become a topological superfluid with Majorana edge states. As the interaction is quenched near the topological phase boundary, we identify an interesting dynamical phase transition of the quenched state in the long-time limit, characterized by an abrupt change of the pairing gap at a critical quenched interaction strength. We further demonstrate the topological nature of this dynamical phase transition from edge-state analysis of the quenched states. Our findings provide interesting clues for the understanding of topological phase transitions in dynamical processes, and can be useful for the dynamical detection of Majorana edge states in corresponding systems.

cond-mat.quant-gas↗

arXiv2014

Effect of incommensurate disorder on the resonant tunneling through Majorana bound states on the topological superconductor chains

We study the transport through the Kitaev's chain with incommensurate potentials coupled to two normal leads by the numerical operator method. We find a quantized linear conductance of $e^2/h$, which is independent to the disorder strength and the gate voltage in a wide range, signaling the Majorana bound states. While the incommensurate disorder suppresses the current at finite voltage bias, and then narrows the linear response regime of the $I-V$ curve which exhibits two plateaus corresponding to the superconducting gap and the band edge respectively. The linear conductance abruptly drops to zero as the disorder strength reaches the critical value $2+2Δ$ with $Δ$ the p-wave pairing amplitude, corresponding to the transition from the topological superconducting phase to the Anderson localized phase. Changing the gate voltage will also cause an abrupt drop of the linear conductance by driving the chain into the topologically trivial superconducting phase, whose $I-V$ curve exhibits an exponential shape.

cond-mat.mes-hall↗

arXiv2014

Collective modes of a one-dimensional trapped atomic Bose gas at finite temperatures

We theoretically investigate collective modes of a one-dimensional (1D) interacting Bose gas in harmonic traps at finite temperatures, by using a variational approach and local density approximation. We find that the temperature dependence of collective mode frequencies is notably different in the weakly and strongly interacting regimes. Therefore, the experimental measurement of collective modes could provide a sensitive probe for different quantum phases of a 1D trapped Bose gas, realized by tuning the interatomic interaction strength and temperature. Our prediction on the temperature dependence of the breathing mode frequency is in good qualitative agreement with an earlier experimental measurement for a weakly interacting 1D Bose gas of rubidium-87 atoms in harmonic traps [Moritz et al., Phys. Rev. Lett. 91, 250402 (2003)].

cond-mat.quant-gas↗

arXiv2013

Component separation of two-component fermion clouds in a spin-dependent external potential by spin-density-functional theory

We investigate the component separation in one-dimensional two-component fermion clouds in a spin-dependent external potential. The density distributions and the state diagram are studied by means of spin-dependent density-functional theory. The component separation between spin-up and spin-down atoms is induced by the interplay of the spin-dependent harmonic confinement and the strong repulsive interaction between the inter-components. We find the existence of a threshold repulsive interaction strength above which the component separation evolves. Different state diagrams are mapped out numerically, from which two regions are distinguished, i.e., the phase-mixed region with both spin-up and spin-down mixtures in the center of the trap and the phase-separated region with only spin-up atoms remaining in the center.

cond-mat.str-el↗

arXiv2013

Randomly Fluctuating Potential Controlled Multistable Resonant Tunneling Current through a Quantum Dot

We study the transport through a quantum dot subject to a randomly fluctuating potential, generated by a sequence of pulses in the gate voltage with the help of the autoregressive model. We find that the tunneling current is multistable when the fluctuating potential with a finite correlation time is applied before the non-equilibrium steady state is built up. The non-equilibrium stationary current is heavily dependent on the history of the fluctuating potential during the transient period if the potential has a finite correlation time. Furthermore, the averaged current over the path of the fluctuating potential is a function of its strength and correlation time. Our work therefore provides a robust theoretical proposal for the controlling of the non-equilibrium stationary current through a quantum dot in a randomly fluctuating potential.

cond-mat.mes-hall↗

arXiv2013

Momentum distribution functions in ensembles: the inequivalence of microcannonical and canonical ensembles in a finite ultracold system

It is demonstrated that in many thermodynamic textbooks the equivalence of the different ensembles is achieved in the thermodynamic limit. In this present work we remark the inequivalence of microcannonical and canonical ensembles in a finite ultracold system at low energies. We calculate the microcanonical momentum distribution function (MDF) in a system of identical fermions (bosons). We find that, the microcanonical MDF deviates from the canonical one, which is the Fermi-Dirac (Bose-Einstein) function, in a finite system at low energies where the single-particle density of states and its inverse are finite.

cond-mat.stat-mech↗

arXiv2012

2kF-Friedel to 4kF-Wigner oscillations in one-dimensional Fermi gases under confinement

Density oscillations of confined one-dimensional Fermi gases of contact repulsive interactions in a continuous space are discussed within Bethe-ansatz-based spin-density-functional theory. The results are compared against the exact analytical and the exact diagonalization method. For an unpolarized system, the number of peaks in the density profiles is doubled, signaling the crossover of the 2k_F-Friedel to 4k_F-Wigner oscillations (with kF being the Fermi wave vector). For both unpolarized and polarized systems, a threshold of the short-range interaction strength can be found where Nf-peak Wigner oscillations of a 4k_F wave vector appear in the density profile (N_f is the total particle number).

cond-mat.str-el↗

arXiv2012

The demixing of the two-component fermions in optical lattices under a spin-dependent external potential

The demixing of two-component fermions in optical lattices under a spin-dependent external potential is investigated using the density-matrix renormalization group method. The influence of on-site interactions (u) and the ratio of the spin-dependent external potentials ($γ$) on the demixing is discussed. The $γ-u$ state diagram is numerically mapped out, from which we distinguish the phase-mixed region from the phase-separated one. A minimum point appears in the phase boundary. On the right part of the point an insulating core is formed in the spin-up densities during the demixing, while on the left one only metallic phase exists.

cond-mat.str-el↗

arXiv2012

Wigner crystal versus Fermionization for one-dimensional Hubbard models with and without long-range interactions

The ground state properties of Hubbard model with or without long-range interactions in the regime with strongly repulsive on-site interaction are investigated by means of the exact diagonalization method. We show that the appearance of $N$-crests in the density profile of a trapped N-fermion system is a natural result of "fermionization" between antiparallel-spin fermions in the strongly repulsive limit and can not be taken as the only signature of Wigner crystal phase, as the static structure factor does not show any signature of crystallization. On the contrary, both the density distribution and static structure factor of Hubbard model with strong long-range interactions display clear signature of Wigner crystal. Our results indicate the important role of long-range interaction in the formation of Wigner crystal.

cond-mat.quant-gas↗

arXiv2012

Lattice density functional theory at finite temperature with strongly density-dependent exchange-correlation potentials

The derivative discontinuity of the exchange-correlation (xc) energy at integer particle number is a property of the exact, unknown xc functional of density functional theory (DFT) which is absent in many popular local and semilocal approximations. In lattice DFT, approximations exist which exhibit a discontinuity in the xc potential at half filling. However, due to convergence problems of the Kohn-Sham (KS) self-consistency cycle, the use of these functionals is mostly restricted to situations where the local density is away from half filling. Here a numerical scheme for the self-consistent solution of the lattice KS Hamiltonian with a local xc potential with rapid (or quasi-discontinuous) density dependence is suggested. The problem is formulated in terms of finite-temperature DFT where the discontinuity in the xc potential emerges naturally in the limit of zero temperature. A simple parametrization is suggested for the xc potential of the uniform 1D Hubbard model at finite temperature which is obtained from the solution of the thermodynamic Bethe ansatz. The feasibility of the numerical scheme is demonstrated by application to a model of fermionic atoms in a harmonic trap. The corresponding density profile exhibits a plateau of integer occupation at low temperatures which melts away for higher temperatures.

cond-mat.str-el↗