arXiv subjects

Xiancong Lu

Publications and source records attributed to Xiancong Lu.

18 recordsLinked to original sources

arXiv2026

Many-Body Non-Hermitian Physics in the Generalized Brillouin Zone

The breakdown of conventional bulk-boundary correspondence (BBC) in non-Hermitian system can be resolved by the generalized Brillouin zone (GBZ) theory. However, extending the GBZ theory to interacting many-body systems remains an open problem. Here, we consider an interacting non-Hermitian model characterized by a circular GBZ. We show that, based on a GBZ transformation, a quasi-reciprocal many-body Hamiltonian can be constructed which, under periodic boundary conditions (PBC), captures the physics of the original non-Hermitian model under open boundary conditions (OBC). Using exact diagonalization (ED), we determine the phase diagram for the quasi-reciprocal many-body Hamiltonian by computing the Zak phase and the structure factor of the charge-density-wave (CDW) phase. We further investigate the entanglement properties and find that the degeneracy of the low-lying entanglement spectrum characterizes each phase in the phase diagram. These findings demonstrate that the topological properties in interacting non-Hermitian system is encoded in the entanglement spectrum of the quasi-reciprocal model. Our work establishes a route to studying many-body non-Hermitian physics within the GBZ formalism.

cond-mat.str-el↗

arXiv2025

Spin Splitting Nernst Effect in Altermagnet

Altermagnet is a distinctive magnet phase, which has spin-split energy band but with zero net magnetic moment. In this paper, we propose that altermagnet behaves spin splitting Nernst effect: Under a longitudinal temperature gradient, the electrons with opposite spins tend to split oppositely in the transverse direction, thus generating a transverse spin current. The spin splitting Nernst effect is understood from the contribution of the longitudinal wave vector to the transverse group velocity. Using the nonequilibrium Green's function method, we calculate the spin-dependent transmission coefficient in the four-terminal altermagnet device. From the spin-dependent transmission coefficient, the nonzero transverse spin current from longitudinal temperature gradient is obtained, and the spin splitting Nernst effect is verified. We systematically study the parameter dependence of the spin splitting Nernst effect, while also performing symmetry analysis. The spin splitting Nernst effect can be easily regulated by Fermi surface energy, temperature, transport direction, and system size. Furthermore, in altermagnet, the $xy$-response and $yx$-response spin splitting Nernst coefficients are equal with $N_{s,xy}=N_{s,yx}$, different from the conventional spin Nernst effect where they are opposite. Meanwhile, the spin splitting Nernst effect require neither spin-orbit coupling nor net magnetism.

cond-mat.mes-hall↗

arXiv2024

Third-order Orbital Corner State and its Realization in Acoustic Crystals

Three dimensional (3D) third-order topological insulators (TIs) have zero-dimensional (0D) corner states, which are three dimensions lower than bulk. Here we investigate the third-order TIs on breathing pyrochlore lattices with p-orbital freedom. The tight-binding Hamiltonian is derived for the p-orbital model, in which we find that the two orthogonal ${\pi}$-type (transverse) hoppings are the key to open a band gap and obtain higher-order topological corner states. We introduce the Z4 berry phase to characterize the bulk topology and analysis the phase diagram. The corner states, demonstrated in a finite structure of a regular tetrahedron, exhibit rich 3D orbital configurations. Furthermore, we design an acoustic system to introduce the necessary ${\pi}$-type hopping and successfully observe the orbital corner states. Our work extends topological orbital corner states to third-order, which enriches the contents of orbital physics and may lead to applications in novel topological acoustic devices.

physics.app-ph↗

arXiv2024

Topological phases in twisted Rashba superconductors

We study the topological properties of a twisted superconducting bilayer with spin-singlet pairings and Rashba spin-orbital coupling. By introducing the chirality basis, we obtain the effective odd-parity superconductors with the help of spin-orbital coupling. For the twisted bilayer with $d$-wave pairings, two non-Abelian topological phases with Chern number $C=-1$ and $C=-5$ are identified, and the analytical expressions for the boundary of non-Abelian phase are derived as well within the circular Fermi surface approximation. We perform numerical calculations at the twisted angle of Moir\'e lattice, which further verify the topological phase diagram from the effective odd-parity Hamiltonian. For the bilayer with $d$-wave and $s_{\pm}$-wave pairings, we reveal the second-order topological superconductor with Majorana zero mode on each corner, by analyzing the relative configuration of the pairing nodes of superconductors and the Fermi surface of normal state. It is found that the regions of second-order topological phase are narrowed when the bilayer is twisted.

cond-mat.supr-con↗

arXiv2024

Entangelment Entropy on Generalized Brillouin Zone

We investigate the entanglement properties of non-Hermitian Su-Schrieffer-Heeger (SSH) model from the perspective of the Generalized Brillouin Zone (GBZ). The non-Bloch entanglement entropy is defined on a quasi-reciprocal lattice, obtained by performing an ordinary Fourier transformation on the non-Bloch Hamiltonian. We demonstrate that the broken bulk-boundary correspondence is recovered in terms of the non-Bloch entanglement entropy. When the GBZ is circular, we show that the non-Bloch entanglement entropy is well-defined (real and positive-definite) in large parameter regions, except close to the exceptional points (EPs). In the critical region, we found that each Fermi point contributes precisely 1 to the central charge $c$ of the logarithmic scaling. At the EP, the central charge becomes negative due to the presence of the exceptional bound state. For the case of non-circular GBZ, long-range hopping emerges in the quasi-reciprocal lattice, and the von Neumann entropy on the GBZ is no longer real. However, the non-Bloch edge entanglement entropy remains real, which serves as a reliable topological indicator and respects the bulk-boundary correspondence. We compute the topological phase diagram, and reveal the critical behavior along the exceptional phase boundaries.

cond-mat.mes-hall↗

arXiv2022

Characterizing the Bulk-Boundary Correspondence of one-dimensional non-Hermitian interacting systems by edge entanglement entropy

Dramatically different from the Hermitian systems, the conventional Bulk-Boundary Correspondence (BBC) is broken in the non-Hermitian systems. In this article, we use edge entanglement entropy to characterize the topological properties of non-Hermitian Su-Schrieffer-Heeger Hubbard model. For free Fermions, we study the scaling behavior of entanglement entropy and demonstrate that the edge entanglement entropy is a good indicator to delimit different phases of non-Hermitian systems. We further generalize the edge entanglement entropy to the non-Hermitian interacting Hubbard chain, and obtain the topological phase diagram in the plane of interaction and non-Hermitian hopping amplitudes. It is found that the Hubbard interaction diminishes and weakens the breakdown of Bulk-Boundary Correspondence, which eventually disappears at some critical value of interaction.

cond-mat.str-el↗

arXiv2021

Doping phase diagram of a Hubbard model for twisted bilayer cuprates

We study the twisted Hubbard model of a cuprate bilayer at a fixed twist angle $θ=53.13^{\circ}$ using the variational cluster approximation, a method that treats short-range dynamical correlations exactly. At intermediate interlayer tunneling, the phase difference $ϕ$ between the $d$-wave order parameters of two layers is $π$ in the overdoped regime, while it is zero in the underdoped regime, close to the Mott phase. At strong interlayer tunneling, we observe a clear time-reversal symmetry breaking phase near optimal doping, in which the phase difference $ϕ$ changes continuously from 0 to $π$. However, this phase has trivial topology. We also apply a cluster extension of dynamical mean field theory to the same problem, but fail to detect a time-reversal breaking phase with that method.

cond-mat.str-el↗

arXiv2021

Spin texture in a bilayer high-temperature cuprate superconductor

We investigate the possibility of spin texture in the bilayer cuprate superconductor $\rm Bi_2Sr_2CaCu_2O_{8+δ}$ using cluster dynamical mean field theory (CDMFT). The one-band Hubbard model with a small interlayer hopping and a Rashba spin-orbit coupling is used to describe the material. The $d$-wave order parameter is not much affected by the presence of the Rashba coupling, but a small triplet component appears. We find a spin texture circulating in the same direction around $\mathbf{k}=(0,0)$ and $\mathbf{k}=(π,π)$ and stable against the superconducting phase. The amplitude of the spin structure, however, is strongly affected by the pseudogap phenomenon, more so than the spectral function itself.

cond-mat.str-el↗

arXiv2021

Higher-order topological phases in tunable $C_3$-symmetric photonic crystals

We demonstrate that multiple higher-order topological transitions can be triggered via the continuous change of the geometry in kagome photonic crystals composed of three dielectric rods. By tuning a single geometry parameter, the photonic corner and edge states emerge or disappear with the higher-order topological transitions. Two distinct higher-order topological insulator phases and a normal insulator phase are revealed. Their topological indices are obtained from symmetry representations. A photonic analog of fractional corner charge is introduced to distinguish the two higher-order topological insulator phases. Our predictions can be readily realized and verified in configurable dielectric photonic crystals.

physics.optics↗

arXiv2020

Loop currents in ladder cuprates: A dynamical mean field theory study

We investigate the possibility of spontaneous loop currents in the two-leg ladder cuprate Sr$_{14-x}$Ca$_x$Cu$_{24}$O$_{41}$ by applying cluster dynamical mean field theory (CDMFT) to a seven-band Hubbard model for that compound, with an exact diagonalization solver. We sample several values of the local interaction $U_d$ and of the Cu-O energy difference $E_{pd}$, by applying an external field that induces loop currents. We find no instance of spontaneous loop currents once the external field is brought to zero.

cond-mat.str-el↗

arXiv2019

Proximity effect in a heterostructure of a high $T_c$ superconductor with a topological insulator from Dynamical mean field theory

We investigate the proximity effect in a heterostructure of the topological insulator (TI) \BiSe\ deposited on the HTSC material BSCCO. The latter is described by the one-band Hubbard model and is treated with cluster dynamical mean field theory (CDMFT), the TI layers being included via the CDMFT self-consistency loop. The penetration of superconductivity into the TI depends on the position of the Fermi level with respect to the TI gap. We illustrate the back action of the TI layer on the HTSC layer, in particular the gradual disappearance of Mott physics with increasing tunneling amplitude.

cond-mat.supr-con↗

arXiv2018

Parity-mixing superconducting phase in the Rashba-Hubbard model and its topological properties from dynamical mean field theory

We investigate parity-mixing superconductivity in the two-dimensional Hubbard model with Rashba spin-orbit coupling, using Cellular Dynamical Mean-Field Theory (CDMFT). A superconducting state with mixed singlet $d$-wave and triplet $p$-wave character is found in a wide range of doping. The singlet component decreases with the amplitude of the Rashba spin-orbit coupling, whereas the triplet component increases, but both disappear at about 20\% doping. The effect of a Zeeman field is also investigated; it tends to suppress both types of superconductivity, but induces nontrivial topological properties: the computed bulk Chern number is nonzero in the mixed superconductivity phase, at least in the underdoped region. A strong suppression of the excitation gap occurs slightly after optimal doping; this might be the sign of a topological transition within the superconducting dome.

cond-mat.supr-con↗

arXiv2011

Time-reversal symmetry breaking phase in the Hubbard model: a VCA study

We study the stability of the time-reversal symmetry breaking staggered flux phase of a single band Hubbard model, within the Variational Cluster Approach (VCA). For intermediate and small values of the interaction $U$, we find metastable solutions for the staggered flux phase, with a maximum current per bond at $U\approx 3.2$. However, allowing for antiferromagnetic and superconducting long-range order it turns out that in the region at and close to half filling the antiferromagnetic phase is the most favorable energetically. The effect of nearest-neighbour interaction is also considered. Our results show that a negative nearest-neighbour interaction and finite doping favors the stability of the staggered-flux phase. We also present preliminary results for the three-band Hubbard model obtained with a restricted set of variational parameters. For this case, no spontaneous time-reversal symmetry breaking phase is found in our calculations.

cond-mat.str-el↗

arXiv2011

Violation of a Bell inequality in two-dimensional spin-orbit hypoentangled subspaces

Based on spin-orbit coupling induced by q-plates, we present a feasible experimental proposal for preparing two-dimensional spatially inhomogeneous polarizations of light. We further investigate the quantum correlations between these inhomogeneous polarizations of photon pairs generated by spontaneous parametric down-conversion, which in essence describe the so-called hypoentanglement that is established between composite spin-orbit variables of photons. The violation of the Clauser-Horne-Shimony-Holt-Bell inequality is predicted with S=2\sqrt2 to illustrate the entangled nature of the cylindrical symmetry of spatially inhomogeneous polarizations.

quant-ph↗

arXiv2009

Dispersive spectrum and orbital order of spinless p-band fermions in an optical lattice

We study single-particle properties of a spinless p-band correlated fermionic gas in an optical lattice by means of a variational cluster approach (VCA). The single-particle spectral function is almost flat at half-filling and develops a strongly dispersive behavior at lower fillings. The competition between different orbital orderings is studied as a function of filling. We observe that an ``antiferromagnetic'' orbital order develops at half-filling and is destroyed by doping the system evolving into a disordered orbital state. At low filling limit, we discuss the possibility of ``ferromagnetic'' orbital order by complementing the VCA result with observations based on a trial wave function. We also study the behavior of the momentum distribution for different values of the on-site interaction. Finally, we introduce an integration contour in the complex plane which allows to efficiently carry out Matsubara-frequency sums.

cond-mat.str-el↗

arXiv2006

Finite-temperature effects on the number fluctuation of ultracold atoms across the Superfluid to Mott-insulator transition

We study the thermodynamics of ultracold Bose atoms in optical lattices by numerically diagonalizing the mean-field Hamiltonian of the Bose-Hubbard model. This method well describes the behavior of long-range correlations and therefore is valid deep in the superfluid phase. For the homogeneous Bose-Hubbard model, we draw the finite-temperature phase diagram and calculate the superfluid density at unity filling. We evaluate the finite-temperature effects in a recent experiment probing number fluctuation [Phys. Rev. Lett. \textbf{96}, 090401 (2006)], and find that our finite-temperature curves give a better fitting to the experimental data, implying non-negligible temperature effects in this experiment.

cond-mat.other↗

arXiv2006

Number Statistics of Ultracold Bosons in Optical Lattice

We study the number statistics of ultracold bosons in optical Lattice using the slave particle technique and quantum Monte Carlo simulations. For homogeneous Bose-Hubbard model, we use the slave particle technique to obtain the number statistics near the superfluid to normal-liquid phase transition. The qualitatively behavior agree with the recent experiment probing number fluctuation [Phys. Rev. Lett. \textbf{96}, 090401 (2006)]. We also perform quantum Monte Carlo simulations to 1D system with external harmonic trap. The results qualitatively agree with the experiments.

cond-mat.str-el↗

arXiv2006

Slave particle approach to the finite temperature properties of ultracold Bose gases in optical lattices

By using slave particle (slave boson and slave fermion) technique on the Bose-Hubbard model, we study the finite temperature properties of ultracold Bose gases in optical lattices. The phase diagrams at finite temperature are depicted by including different types of slave particles and the effect of the finite types of slave particles is estimated. The superfluid density is evaluated using the Landau second order phase transition theory. The atom density, excitation spectrum and dispersion curve are also computed at various temperatures, and how the Mott-insulator evolves as the temperature increases is demonstrated. For most quantities to be calculated, we find that there are no qualitatively differences in using the slave boson or the slave fermion approaches. However, when studying the stability of the mean field state, we find that in contrast to the slave fermion approach, the slave boson mean field state is not stable. Although the slave boson mean field theory gives a qualitatively correct phase boundary, it corresponds to a local maximum of Landau free energy and can not describe the second order phase transition because the coefficient $a_4$ of the fourth order term is always negative in the free energy expansion.

cond-mat.stat-mech↗