Ground-state (GS) properties of the two-dimensional (2D) quantum compass model in an external field on a square 5 × 5 lattice are investigated by using the exact diagonalization (ED) method. We obtain the GS energy and evaluate quantities such as its correlation functions, nearest-neighbor entanglement and local order parameter. As the external field is presented, the first-order quantum phase point is absent and the system exhibits the behaviors of the second-order phase transition.
Ground-state (GS) properties of the two-dimensional (2D) quantum compass model in an external field on a square 5 × 5 lattice are investigated by using the exact diagonalization (ED) method. We obtain the GS energy and evaluate quantities such as its correlation functions, nearest-neighbor entanglement and local order parameter. As the external field is presented, the first-order quantum phase point is absent and the system exhibits the behaviors of the second-order phase transition.
The matrix product state (MPS) is utilized to study the ground-state properties and quantum phase transitions (QPTs) of the one-dimensional extended quantum compass model (EQCM). The MPS wave functions are argued to be very efficient descriptions of the 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 detail. It is revealed that the von Neumann entanglement entropy, 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 wave function and found to be doubly degenerate in disordered phases, where nonzero string order parameters exist. Moreover, with the linearized tensor renormalization group method, the specific-heat curves are evaluated and their low-temperature behaviors are investigated. Compared with the exact solutions, our results verify that these MPS-based numerical methods are very accurate and powerful, and can be employed to investigate other EQCMs which do not permit exact solutions at present.
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.
By Lanczos exact diagonalization and the infinite time-evolving block decimation (iTEBD) technique, the two-site entanglement as well as the bipartite entanglement, the ground state energy, the nearest-neighbor correlations, and the magnetization in the antiferromagnetic Heisenberg (AFH) model under an external field are investigated. With increasing external field, the small size system shows some distinct upward magnetization stairsteps, accompanied synchronously with some downward two-site entanglement stairsteps. In the thermodynamic limit, the two-site entanglement, as well as the bipartite entanglement, the ground state energy, the nearest-neighbor correlations, and the magnetization are calculated, and the critical magnetic field h(c) = 2.0 is determined exactly. Our numerical results show that the quantum entanglement is sensitive to the subtle changing of the ground state, and can be used to describe the magnetization and quantum phase transition. Based on the discontinuous behavior of the first-order derivative of the entanglement entropy and fidelity per site, we think that the quantum phase transition in this model should belong to the second-order category. Furthermore, in the magnon existence region (h < 2.0), a logarithmically divergent behavior of block entanglement which can be described by a free bosonic field theory is observed, and the central charge c is determined to be 1.
We investigate the anisotropic quantum orbital compass model on an infinite square lattice by means of the infinite projected entangled-pair state algorithm. For varying values of the Jx and Jz coupling constants of the model, we approximate the ground state and evaluate quantities such as its expected energy and local order parameters. We also compute adiabatic continuations of the ground state, and show that several ground states with different local properties coexist at Jx=Jz. All our calculations are fully consistent with a first order quantum phase transition at this point, thus corroborating previous numerical evidence. Our results also suggest that tensor network algorithms are particularly fitted to characterize first order quantum phase transitions.
Quantum phase transitions in the one-dimensional period-two and uniform quantum compass model are studied by using the pseudospin transformation method and the trace map method. The exact solutions are presented, the fidelity, the nearest-neighbor pseudospin entanglement, spin and pseudospin-correlation functions are then calculated. At the critical point, the fidelity and its susceptibility change substantially, the gap of pseudospin concurrence is observed, which scales as 1/N (N is the system size). The spin-correlation functions show smooth behavior around the critical point. In the period-two chain, the pseudospin-correlation functions exhibit an oscillating behavior, which is absent in the uniform chain. The divergent correlation length at the critical point is demonstrated in the general trend for both cases.
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.