One-dimensional Quantum Compass Model Research Articles

Dissipative spin chain as a non-Hermitian Kitaev ladder

We derive exact results for the Lindblad equation for a quantum spin chain (one-dimensional quantum compass model) with dephasing noise. The system possesses doubly degenerate nonequilibrium steady states due to the presence of a conserved charge commuting with the Hamiltonian and Lindblad operators. We show that the system can be mapped to a non-Hermitian Kitaev model on a two-leg ladder, which is solvable by representing the spins in terms of Majorana fermions. This allows us to study the Liouvillian gap, the inverse of relaxation time, in detail. We find that the Liouvillian gap increases monotonically when the dissipation strength $ \gamma $ is small, while it decreases monotonically for large $ \gamma $, implying a kind of phase transition in the first decay mode. The Liouvillian gap and the transition point are obtained in closed form in the case where the spin chain is critical. We also obtain the explicit expression for the autocorrelator of the edge spin. The result implies the suppression of decoherence when the spin chain is in the topological regime.

Geometric phase and the influence of the Dzyaloshinski–Moriya interaction in the one-dimensional quantum compass model

Geometric phase and quantum phase transition (QPT) of the one-dimensional (1D) quantum compass model with the Dzyaloshinski–Moriya (DM) interaction are investigated, and the effect of the DM interaction to the properties of geometric phase and QPTs of the model are discussed in this paper. Our study is an extension of the relation between the geometric phase and QPTs in the 1D spin systems.

Long-range string orders and topological quantum phase transitions in the one-dimensional quantum compass model

In order to investigate the quantum phase transition in the one-dimensional quantum compass model, we numerically calculate non-local string correlations, entanglement entropy and fidelity per lattice site by using the infinite matrix product state representation with the infinite time evolving block decimation method. In the whole range of the interaction parameters, we find that four distinct string orders characterize the four different Haldane phases and the topological quantum phase transition occurs between the Haldane phases. The critical exponents of the string order parameters β = 1/8 and the cental charges c = 1/2 at the critical points show that the topological phase transitions between the phases belong to an Ising type of universality classes. In addition to the string order parameters, the singularities of the second derivative of the ground state energies per site, the continuous and singular behaviors of the Von Neumann entropy and the pinch points of the fidelity per lattice site manifest that the phase transitions between the phases are of the second-order, in contrast to the first-order transition suggested in previous studies.

Multicritical Point in the One-dimensional Quantum Compass Model

Multicritical Point in the One-dimensional Quantum Compass Model

Matrix product state and quantum phase transitions in the one-dimensional extended quantum compass model

The matrix product state (MPS) is utilized to study the ground state properties and quantum phase transitions (QPTs) of the one-dimensional quantum compass model (QCM). The MPS wavefunctions are argued to be very efficient descriptions of QCM ground states, and are numerically determined by imaginary time projections. The ground state energy, correlations, quantum entanglement and its spectrum, local and nonlocal order parameters, etc., are calculated and studied in details. It is revealed that the bipartite and block entanglement entropies, as well as the nearest neighbor correlation functions can be used to detect the second-order QPTs, but not the first-order ones, while fidelity detections can recognize both. The entanglement spectrum is extracted from the MPS wavefunction, and found to be doubly degenerate in disordered phases of QCM, where non-local string order parameters exist. Moreover, with linearized tensor renormalization group method, the specific heat curves are evaluated and their low temperature behaviors are investigated.

Bipartite entanglement of the one-dimensional extended quantum compass model in a transverse field

By using the infinite time-evolving block decimation (iTEBD) method, we obtain the ground state wave function of the one-dimensional quantum compass model in a transverse field in the form of a matrix product state (MPS). Based on the MPS, quantum entanglement, order parameters, and correlation functions are calculated numerically. The bipartite entanglement measure which is defined by the singular values obtained from the singular value decomposition (SVD) of tensors is found to be capable of detecting all the quantum phase transitions in this model. The rich phase diagram that we have obtained supports that suggested previously by using the Jordan-Wigner transformation. In addition, some order parameters used to characterise different phases are also introduced.

Quantum correlation in one-dimensional extended quantum compass model

We study the correlations in the one-dimensional extended quantum compass model in a transverse magnetic field. By exactly solving the Hamiltonian, we find that the quantum correlation of the ground state of one-dimensional quantum compass model is vanishing. We show that quantum discord can not only locate the quantum critical points, but also discern the orders of phase transitions. Furthermore, entanglement quantified by concurrence is also compared.

One-Dimensional Quantum Compass Model in an Out-plane Magnetic Field

The one-dimensional quantum compass model (1D-QCM) in an out-plane magnetic field is investigated by numerical and analytical methods. The presence of the 1D-QCM in an area of the ground-state magnetic phase diagram where the odd couplings are antiferromagnetic and larger than the even couplings is studied. Using pseudo spin ladder operators indicates that the 1D-QCM in an out-plane magnetic field can be mapped to the one-dimensional Ising model in a transverse magnetic field (ITF). Analytical investigation of the effective ITF Hamiltonian predicts the occurrence of two quantum phase transitions with increasing magnetic field. Also, the critical fields are obtained from this method, which are completely in agreement with the results of the numerical experiment based on the Lanczos method. This numerical method accurately determined the behavior of the energy gap, magnetization and string order parameter, and therefore it is a very useful method for indicating the ground-state phases of the system.

Numerical study of the one-dimensional quantum compass model

The ground state magnetic phase diagram of the one-dimensional quantum compass model (QCM) is studied using the numerical Lanczos method. A detailed numerical analysis of the low energy excitation spectrum is presented. The energy gap and the spin-spin correlation functions are calculated for finite chains. Two kind of the magnetic long-range orders, the Neel and a type of the stripe-antiferromagnet, in the ground state phase diagram are identified. Based on the numerical analysis, the first and second order quantum phase transitions in the ground state phase diagram are identified.

Multicriticality and entanglement in the one-dimensional quantum compass model

We study the one-dimensional quantum compass model with two independent parameters by means of an exact mapping to the quantum Ising model. This allows us to uncover hidden features of the quantum phase transition in the ordinary one-parameter quantum compass model, showing that it occurs at a multicritical point where a line of first-order transitions intersects a line of second-order symmetry-breaking transitions of Ising type. We calculate the concurrence and the block entanglement entropy in the four ground-state phases and find that these entanglement measures accurately signal the second-order, but not the first-order, transitions.