arXiv subjects

Junpeng Cao

Publications and source records attributed to Junpeng Cao.

At least 37 records · Page 2Linked to original sources

arXiv2023

Localization and mobility edges in non-Hermitian disorder-free lattices

The non-Hermitian skin effect (NHSE) is a significant phenomenon observed in non-Hermitian systems under open boundary conditions, where the extensive bulk eigenstates tend to accumulate at the lattice edges. In this article, we investigate how an electric field affects the localization properties in a non-Hermitian mosaic Stark lattice, exploring the interplay between the Stark localization, mobility edge (ME), and the NHSE induced by nonreciprocity. We analytically obtain the Lyapunov exponent and the phase transition points as well as numerically calculate the density distributions and the spectral winding number. We reveal that in the nonreciprocal Stark lattice with the mosaic periodic parameter $κ=1$, there exists a critical electric field strength that describes the transition of the existence-nonexistence of NHSE and is inversely proportional to the lattice size. This transition is consistent with the real-complex transition and topological transition characterized by spectral winding number under periodic boundary conditions. In the strong fields, the Wannier-Stark ladder is recovered, and the Stark localization is sufficient to suppress the NHSE. When the mosaic period $κ=2$, we show that the system manifests an exact non-Hermitian ME and the skin states are still existing in the strong fields, in contrast to the gigantic field can restrain the NHSE in the $κ=1$ case. Moreover, we further study the expansion dynamics of an initially localized state and dynamically probe the existence of the NHSE and the non-Hermitian ME. These results could help us to control the NHSE and the non-Hermitian ME by using electric fields in the disorder-free systems.

cond-mat.dis-nn↗

arXiv2023

Multiple localization transitions and novel quantum phases induced by staggered on-site potential

We propose an one-dimensional generalized Aubry-Andr{é}-Harper (AAH) model with off-diagonal hopping and staggered on-site potential. We find that the localization transitions could be multiple reentrant with the increasing of staggered on-site potential. The multiple localization transitions are verified by the quantum static and dynamic measurements such as the inversed or normalized participation ratios, fractal dimension and survival probability. Based on the finite-size scaling analysis, we also obtain an interesting intermediate phase where the extended, localized and critical states are coexistent in certain regime of model parameters. These results are quite different from those in the generalized AAH model with off-diagonal hopping, and can help us to find novel quantum phases, new localization phenomena in the disordered systems.

cond-mat.dis-nn↗

arXiv2023

Spectrum of the transfer matrices of the spin chains associated with the $A^{(2)}_3$ Lie algebra

We study the exact solution of quantum integrable system associated with the $A^{(2)}_3$ twist Lie algebra, where the boundary reflection matrices have non-diagonal elements thus the $U(1)$ symmetry is broken. With the help of the fusion technique, we obtain the closed recursive relations of the fused transfer matrices. Based on them, together with the asymptotic behaviors and the values at special points, we obtain the eigenvalues and Bethe ansatz equations of the system. We also show that the method is universal and valid for the periodic boundary condition where the $U(1)$ symmetry is reserved. The results in this paper can be applied to studying the exact solution of the $A^{(2)}_n$-related integrable models with arbitrary $n$.

math-ph↗

arXiv2023

Exact solution of the $q$-deformed $D^{(1)}_3$ vertex model with open boundaries

In this paper, we study the exact solution of the $q$-deformed $D^{(1)}_3$ quantum lattice model with non-diagonal open boundary condition. We demonstrate the crossing symmetry of the transfer matrix and obtain the quantum determinant. We construct the independent transfer matrix fusion identities and show that the fusion processes can be closed. Based on the fusion hierarchies and polynomial analysis, we obtain the inhomogeneous $T-Q$ relations, exact energy spectrum and Bethe ansatz equations of the system.

math-ph↗

arXiv2023

Elementary excitations in an integrable twisted J1-J2 spin chain in the thermodynamic limit

The exact elementary excitations in a typical U(1) symmetry broken quantum integrable system, that is the twisted J1-J2 spin chain with nearest-neighbor, next nearest neighbor and chiral three spin interactions, are studied. The main technique is that we quantify the energy spectrum of the system by the zero roots of transfer matrix instead of the traditional Bethe roots. From the numerical calculation and singularity analysis, we obtain the patterns of zero roots. Based on them, we analytically obtain the ground state energy and the elementary excitations in the thermodynamic limit. We find that the system also exhibits the nearly degenerate states in the regime of $η\in \mathbb{R}$, where the nearest-neighbor couplings among the z-direction are ferromagnetic. More careful study shows that the competing of interactions can induce the gapless low-lying excitations and quantum phase transition in the antiferromagnetic regime with $η\in \mathbb{R}+iπ$.

math-ph↗

arXiv2022

Off-diagonal Bethe Ansatz for the $D^{(1)}_3$ model

The exact solutions of the $D^{(1)}_3$ model (or the $so(6)$ quantum spin chain) with either periodic or general integrable open boundary conditions are obtained by using the off-diagonal Bethe Ansatz. From the fusion, the complete operator product identities are obtained, which are sufficient to enable us to determine spectrum of the system. Eigenvalues of the fused transfer matrices are constructed by the $T-Q$ relations for the periodic case and by the inhomogeneous $T-Q$ one for the non-diagonal boundary reflection case. The present method can be generalized to deal with the $D^{(1)}_{n}$ model directly.

math-ph↗

arXiv2022

Exact surface energy of the $D^{(1)}_2$ spin chain with generic non-diagonal boundary reflections

The exact solution of the $D^{(1)}_2$ quantum spin chain with generic non-diagonal boundary reflections is obtained. It is found that the generating functional of conserved quantities of the system can be factorized as the product of transfer matrices of two anisotropic $XXZ$ spin chains with open boundary conditions. By using the factorization identities and the fusion technique, the eigenvalues and the Bethe ansatz equations of the model are obtained. The eigenvalues are also parameterized by the zero roots of the transfer matrix, and the patterns of root distributions are obtained. Based on them, ground states energy and the surface energies induced by the twisted boundary magnetic fields in the thermodynamic limit are obtained. These results are checked by the numerical calculations. The corresponding isotropic limit is also discussed. The results given in this paper are the foundation to study the exact physical properties of high rank $D^{(1)}_{n}$ model by using the nested processes.

math-ph↗

arXiv2022

Spectrum of the quantum integrable $D^{(2)}_2$ spin chain with generic boundary fields

Exact solution of the quantum integrable $D^{(2)}_2$ spin chain with generic integrable boundary fields is constructed. It is found that the transfer matrix of this model can be factorized as the product of those of two open staggered anisotropic XXZ spin chains. Based on this identity, the eigenvalues and Bethe ansatz equations of the $D^{(2)}_2$ model are derived via off-diagonal Bethe ansatz.

math-ph↗

arXiv2022

Exact solution of the quantum integrable model associated with the twisted $D^{(2)}_3$ algebra

We generalize the nested off-diagonal Bethe ansatz method to study the quantum chain associated with the twisted $D^{(2)}_3$ algebra (or the $D^{(2)}_3$ model) with either periodic or integrable open boundary conditions. We obtain the intrinsic operator product identities among the fused transfer matrices and find a way to close the recursive fusion relations, which makes it possible to determinate eigenvalues of transfer matrices with an arbitrary anisotropic parameter $η$. Based on them, and the asymptotic behaviors and values at certain points, we construct eigenvalues of transfer matrices in terms of homogeneous $T-Q$ relations for the periodic case and inhomogeneous ones for the open case with some off-diagonal boundary reflections. The associated Bethe ansatz equations are also given. The method and results in this paper can be generalized to the $D^{(2)}_{n+1}$ model and other high rank integrable models.

math-ph↗

arXiv2022

Thermodynamic limit and boundary energy of the spin-1 Heisenberg chain with non-diagonal boundary fields

The thermodynamic limit and boundary energy of the isotropic spin-1 Heisenberg chain with non-diagonal boundary fields are studied. The finite size scaling properties of the inhomogeneous term in the $ T-Q $ relation at the ground state are calculated by the density matrix renormalization group. Based on our findings, the boundary energy of the system in the thermodynamic limit can be obtained from Bethe ansatz equations of a related model with parallel boundary fields. These results can be generalized to the $SU(2)$ symmetric high spin Heisenberg model directly.

hep-th↗

arXiv2022

Exact ground state and elementary excitations of a competing spin chain with twisted boundary condition

A novel Bethe ansatz scheme is proposed to investigate the exact physical properties of an integrable anisotropic quantum spin chain with competing interactions among the nearest, next nearest neighbor and chiral three spin couplings, where the boundary condition is the twisted one. The eigenvalue of the transfer matrix is characterized by its zero roots instead of the traditional Bethe roots. Based on the exact solution, the conserved momentum and charge operators of this U(1)-symmetry broken system are obtained. The ground state energy and density of rapidities are calculated. It is found that there exist three kinds of elementary excitations and the corresponding dispersion relations are obtained, which gives a different picture from that with periodic boundary condition.

math-ph↗

arXiv2021

Scattering matrix of elementary excitations in the antiperiodic XXZ spin chain with η=iπ/3

We study the thermodynamic limit of the antiperiodic XXZ spin chain with the anisotropic parameter $η=\frac{πi}{3}$. We parameterize eigenvalues of the transfer matrix by their zero points instead of Bethe roots. We obtain patterns of the distribution of zero points. Based on them, we calculate the ground state energy and the elementary excitations in the thermodynamic limit. We also obtain the two-body scattering matrix of elementary excitations. Two types of elementary excitations and three types of scattering processes are discussed in detailed.

math-ph↗

arXiv2021

Root patterns and energy spectra of quantum integrable systems without $U(1)$ symmetry: antiperiodic $XXZ$ spin chain

Finding out root patterns of quantum integrable models is an important step to study their physical properties in the thermodynamic limit. Especially for models without $U(1)$ symmetry, their spectra are usually given by inhomogeneous $T-Q$ relations and the Bethe root patterns are still unclear. In this paper with the antiperiodic $XXZ$ spin chain as an example, an analytic method to derive both the Bethe root patterns and the transfer-matrix root patterns in the thermodynamic limit is proposed. Based on them the ground state energy and elementary excitations in the gapped regime are derived. The present method provides an universal procedure to compute physical properties of quantum integrable models in the thermodynamic limit.

math-ph↗

arXiv2021

Surface energy of the one-dimensional supersymmetric $t-J$ model with general integrable boundary terms in the antiferromagnetic sector

In this paper, we study the surface energy of the one-dimensional supersymmetric $t-J$ model with unparallel boundary magnetic fields, which is a typical $U(1)$-symmetry broken quantum integrable strongly correlated electron system. It is shown that at the ground state, the contribution of inhomogeneous term in the Bethe ansatz solution of eigenvalues of transfer matrix satisfies the finite size scaling law $L^β$ where $β<0$. Based on it, the physical quantities of the system in the thermodynamic limit are calculated. We obtain the patterns of Bethe roots and the analytical expressions of density of states, ground state energy and surface energy. We also find that there exist the stable boundary bound states if the boundary fields satisfy some constraints.

math-ph↗

arXiv2021

T-W relation and free energy of the Heisenberg chain at a finite temperature

A new nonlinear integral equation (NLIE) describing the thermodynamics of the Heisenberg spin chain is derived based on the t-W relation of the quantum transfer matrices. The free energy of the system in a magnetic field is thus obtained by solving the NLIE. This method can be generalized to other lattice quantum integrable models. Taking the SU(3)-invariant quantum spin chain as an example, we construct the corresponding NLIEs and compute the free energy. The present results coincide exactly with those obtained via other methods previously.

math-ph↗

arXiv2021

Exact surface energy and helical spinons in the XXZ spin chain with arbitrary non-diagonal boundary fields

An analytic method is proposed to compute the surface energy and elementary excitations of the XXZ spin chain with generic non-diagonal boundary fields. For the gapped case, in some boundary parameter regimes the contributions of the two boundary fields to the surface energy are non-additive. Such a correlation effect between the two boundaries also depends on the parity of the site number $N$ even in the thermodynamic limit $N\to\infty$. For the gapless case, contributions of the two boundary fields to the surface energy are additive due to the absence of long-range correlation in the bulk. Although the $U(1)$ symmetry of the system is broken, exact spinon-like excitations, which obviously do not carry spin-$\frac12$, are observed. The present method provides an universal procedure to deal with quantum integrable systems either with or without $U(1)$ symmetry.

cond-mat.stat-mech↗

arXiv2021

Exact solutions of the $C_n$ quantum spin chain

We study the exact solutions of quantum integrable model associated with the $C_n$ Lie algebra, with either a periodic or an open one with off-diagonal boundary reflections, by generalizing the nested off-diagonal Bethe ansatz method. Taking the $C_3$ as an example we demonstrate how the generalized method works. We give the fusion structures of the model and provide a way to close fusion processes. Based on the resulted operator product identities among fused transfer matrices and some necessary additional constraints such as asymptotic behaviors and relations at some special points, we obtain the eigenvalues of transfer matrices and parameterize them as homogeneous $T-Q$ relations in the periodic case or inhomogeneous ones in the open case. We also give the exact solutions of the $C_n$ model with an off-diagonal open boundary condition. The method and results in this paper can be generalized to other high rank integrable models associated with other Lie algebras.

math-ph↗

arXiv2020

Thermodynamic limit of the spin-$\frac{1}{2}$ XYZ spin chain with the antiperiodic boundary condition

Based on its off-diagonal Bethe ansatz solution, we study the thermodynamic limit of the spin-$\frac{1}{2}$ XYZ spin chain with the antiperiodic boundary condition. The key point of our method is that there exist some degenerate points of the crossing parameter $η_{m,l}$, at which the associated inhomogeneous $T-Q$ relation becomes a homogeneous one. This makes extrapolating the formulae deriving from the homogeneous one to an arbitrary $η$ with $O(N^{-2})$ corrections for a large $N$ possible. The ground state energy and elementary excitations of the system are obtained. By taking the trigonometric limit, we also give the results of antiperiodic XXZ spin chain within the gapless region in the thermodynamic limit, which does not have any degenerate points.

math-ph↗