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Junpeng Cao

Publications and source records attributed to Junpeng Cao.

At least 91 records · Page 5Linked to original sources
arXiv2014

Exact solution of the Izergin-Korepin model with general non-diagonal boundary terms

The Izergin-Korepin model with general non-diagonal boundary terms, a typical integrable model beyond A-type and without U(1)-symmetry, is studied via the off-diagonal Bethe ansatz method. Based on some intrinsic properties of the R-matrix and the K-matrices, certain operator product identities of the transfer matrix are obtained at some special points of the spectral parameter. These identities and the asymptotic behaviors of the transfer matrix together allow us to construct the inhomogeneous T-Q relation and the associated Bethe ansatz equations. In the diagonal boundary limit, the reduced results coincide exactly with those obtained via other methods.

math-ph↗
arXiv2014

Spin-1/2 XYZ model revisit: general solutions via off-diagonal Bethe ansatz

The spin-1/2 XYZ model with both periodic and anti-periodic boundary conditions is studied via the off-diagonal Bethe ansatz method. The exact spectra of the Hamiltonians and the Bethe ansatz equations are derived by constructing the inhomogeneous T-Q relations, which allow us to treat both the even N (the number of lattice sites) and odd N cases simultaneously in an unified approach.

cond-mat.stat-mech↗
arXiv2014

Nested off-diagonal Bethe ansatz and exact solutions of the su(n) spin chain with generic integrable boundaries

The nested off-diagonal Bethe ansatz method is proposed to diagonalize multi-component integrable models with generic integrable boundaries. As an example, the exact solutions of the su(n)-invariant spin chain model with both periodic and non-diagonal boundaries are derived by constructing the nested T-Q relations based on the operator product identities among the fused transfer matrices and the asymptotic behavior of the transfer matrices.

hep-th↗
arXiv2014

Thermodynamic limit and surface energy of the XXZ spin chain with arbitrary boundary fields

In two previous papers [26, 27], the exact solutions of the spin-1/2 chains with arbitrary boundary fields were constructed via the off-diagonal Bethe ansatz (ODBA). Here we introduce a method to approach the thermodynamic limit of those models. The key point is that at a sequence of degenerate points of the crossing parameter η=η_m, the off-diagonal Bethe ansatz equations (BAEs) can be reduced to the conventional ones. This allows us to extrapolate the formulae derived from the reduced BAEs to arbitrary ηcase with O(N^{-2}) corrections in the thermodynamic limit N\to\infty. As an example, the surface energy of the XXZ spin chain model with arbitrary boundary magnetic fields is derived exactly. This approach can be generalized to all the ODBA solvable models.

cond-mat.stat-mech↗
arXiv2014

Exact solution of the one-dimensional super-symmetric t-J model with unparallel boundary fields

The exact solution of the one-dimensional super-symmetric t-J model under generic integrable boundary conditions is obtained via the Bethe ansatz methods. With the coordinate Bethe ansatz, the corresponding R-matrix and K-matrices are derived for the second eigenvalue problem associated with spin degrees of freedom. It is found that the second eigenvalue problem can be transformed to that of the transfer matrix of the inhomogeneous XXX spin chain, which allows us to obtain the spectrum of the Hamiltonian and the associated Bethe ansatz equations by the off-diagonal Bethe ansatz method.

math-ph↗
arXiv2013

Exact solution of the one-dimensional Hubbard model with arbitrary boundary magnetic fields

The one-dimensional Hubbard model with arbitrary boundary magnetic fields is solved exactly via the Bethe ansatz methods. With the coordinate Bethe ansatz in the charge sector, the second eigenvalue problem associated with the spin sector is constructed. It is shown that the second eigenvalue problem can be transformed into that of the inhomogeneous XXX spin chain with arbitrary boundary fields which can be solved via the off-diagonal Bethe ansatz method.

cond-mat.str-el↗
arXiv2013

Quantum speed limit for arbitrary initial states

We investigate the generic bound on the minimal evolution time of the open dynamical quantum system. This quantum speed limit time is applicable to both mixed and pure initial states. We then apply this result to the damped Jaynes-Cummings model and the Ohimc-like dephasing model starting from a general time-evolution state. The bound of this time-dependent state at any point in time can be found. For the damped Jaynes-Cummings model, the corresponding bound first decreases and then increases in the Markovian dynamics. While in the non-Markovian regime, the speed limit time shows an interesting periodic oscillatory behavior. For the case of Ohimc-like dephasing model, this bound would be gradually trapped to a fixed value. In addition, the roles of the relativistic effects on the speed limit time for the observer in non-inertial frames are discussed.

quant-ph↗
arXiv2013

Tunable Band Topology Reflected by Fractional Quantum Hall States in Two-Dimensional Lattices

Two-dimensional lattice models subjected to an external effective magnetic field can form nontrivial band topologies characterized by nonzero integer band Chern numbers. In this Letter, we investigate such a lattice model originating from the Hofstadter model and demonstrate that the band topology transitions can be realized by simply introducing tunable longer-range hopping. The rich phase diagram of band Chern numbers is obtained for the simple rational flux density and a classification of phases is presented. In the presence of interactions, the existence of fractional quantum Hall states in both |C|=1 and |C|>1 bands is confirmed, which can reflect the band topologies in different phases. In contrast, when our model reduces to a one-dimensional lattice, the ground states are crucially different from fractional quantum Hall states. Our results may provide insights into the study of new fractional quantum Hall states and experimental realizations of various topological phases in optical lattices.

cond-mat.str-el↗
arXiv2013

Off-diagonal Bethe ansatz solutions of the anisotropic spin-1/2 chains with arbitrary boundary fields

The anisotropic spin-1/2 chains with arbitrary boundary fields are diagonalized with the off-diagonal Bethe ansatz method. Based on the properties of the R-matrix and the K-matrices, an operator product identity of the transfer matrix is constructed at some special points of the spectral parameter. Combining with the asymptotic behavior (for XXZ case) or the quasi-periodicity properties (for XYZ case) of the transfer matrix, the extended T-Q ansatzs and the corresponding Bethe ansatz equations are derived.

cond-mat.stat-mech↗
arXiv2013

Completeness and Bethe root distribution of the spin-1/2 Heisenberg chain with arbitrary boundary fields

Recently, the XXX spin chain with arbitrary boundary fields was successfully solved [1] via the off-diagonal Bethe ansatz method [2]. The correctness and the completeness of this solution were numerically verified by Nepomechie for one choice of the parameterizations [3]. In this paper, we discuss further the completeness of another parameterization of the Bethe ansatz equations and its reduction to the parallel boundary field case. The numerical results show that when the relative angle between the boundary fields turns to zero, both the T-Q relations and the Bethe ansatz equations are reduced to the ones obtained by the conventional Bethe ansatz methods. This allows us to establish a one-to-one correspondence between the Bethe roots of the unparallel boundary field case and those of the parallel boundary field case. In the thermodynamic limit, those two sets of Bethe roots tend to the same and the contribution of the relative angle to the energy is in the order of 1/N.

cond-mat.stat-mech↗
arXiv2013

Off-diagonal Bethe ansatz and exact solution of a topological spin ring

A general method is proposed for constructing the Bethe ansatz equations of integrable models without U(1) symmetry. As an example, the exact spectrum of the XXZ spin ring with M{\" o}bius like topological boundary condition is derived by constructing a modified T-Q relation based on the functional connection between the eigenvalues of the transfer matrix and the quantum determinant of the monodromy matrix. With the exact solution, the elementary excitations of the topological XX spin ring is discussed in detail. It is found that the excitation spectrum indeed shows a nontrivial topological nature.

cond-mat.stat-mech↗
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

Hidden Sp(2s+1)- or SO(2s+1)-symmetry and new exactly solvable models in ultracold atomic systems

The high spin ultracold atom models with a special form of contact interactions, i.e., the scattering lengthes in the total spin-$2,4 \cdots$ channels are equal but may be different from that in the spin-0 channel, is studied. It is found that those models have either $Sp(2s+1)$-symmetry for the fermions or $SO(2s+1)$-symmetry for the bosons in the spin sector. Based on the symmetry analysis, a new class of exactly solvable models is proposed and solved via the Bethe ansatz. The ground states for repulsive fermions are also discussed.

cond-mat.str-el↗
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↗
arXiv2009

Exact Solutions of a One-dimensional Quantum Spin Chain with SO(5)-Symmetry

A new exactly solvable one-dimensional spin-3/2 Heisenberg model with SO(5)-invariance is proposed. The eigenvalues and Bethe ansatz equations of the model are obtained by using the nested algebraic Bethe ansatz approach. Several exotic elementary excitations in the antiferromagnetic region such as neutral spinon with zero spin, heavy spinon with spin-3/2 and dressed spinon with spin-1/2 are found.

cond-mat.str-el↗
arXiv2009

Exact solutions of an SO(5)-invariant spin-3/2 Fermi gas model

An exactly solvable model describing the dilute spin-3/2 fermion gas in one-dimensional optical trap is proposed. The diagonalization of the model Hamiltonian is derived by means of the Bethe ansatz method. Exotic spin excitations such as the heavy spinon with fractional spin 3/2, the neutral spinon with spin zero and the dressed spinon with spin 1/2 are found based on the exact solution.

cond-mat.str-el↗