arXiv subjects

Guang-Shan Tian

Publications and source records attributed to Guang-Shan Tian.

10 recordsLinked to original sources

arXiv2012

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.

cond-mat.str-el↗

arXiv2008

Constrain on possible pairing symmetry in a two-orbital model of FeAs-based superconductors

In this work, we establish a few exact identities through commutation of intra-orbital and inter-orbital on-site pairings with a two-orbital model describing newly discovered FeAs-based superconductors. Applying the conclusion drawn from rigorous relation and physical interpretation, we give constraints on the possible symmetries of the superconducting pairing of the model. Hence the favorable pairings in newly discovered high-temperature oxypnictide superconductors are proposed.

cond-mat.supr-con↗

arXiv2005

Entanglement and quantum phase transitions

We examine several well known quantum spin models and categorize behavior of pairwise entanglement at quantum phase transitions. A unified picture on the connection between the entanglement and quantum phase transition is given.

quant-ph↗

arXiv2005

Local Entanglement and quantum phase transition in spin models

Due to the phase interference of electromagnetic wave, one can recover the total image of one object from a small piece of holograph, which records the interference pattern of two laser light reflected from it. Similarly, the quantum superposition principle allows us to derive the global phase diagram of quantum spin models by investigating a proper local measurement. In the present paper, we study the two-site entanglement in the antifferomagnetic spin models with both spin-1/2 and 1. We show that its behaviors reveal some important information on the global properties and the quantum phase transition of these systems.

quant-ph↗

arXiv2004

The ground state entanglement in the $XXZ$ model

In this paper, we investigate spin entanglement in the $XXZ$ model defined on a $d$-dimensional bipartite lattice. The concurrence, a measure of the entanglement between two spins, is analyzed. We prove rigorously that the ground state concurrence reaches maximum at the isotropic point. For dimensionality $d \ge 2$, the concurrence develops a cusp at the isotropic point and we attribute it to the existence of magnetic long-range order.

quant-ph↗

arXiv2003

Transition from band insulator to Mott insulator in one dimension: Critical behavior and phase diagram

We report a systematic study of the transition from a band insulator (BI) to a Mott insulator (MI) in a one-dimensional Hubbard model at half-filling with an on-site Coulomb interaction U and an alternating periodic site potential V. We employ both the zero-temperature density matrix renormalization group (DMRG) method to determine the gap and critical behavior of the system and the finite-temperature transfer matrix renormalization group method to evaluate the thermodynamic properties. We find two critical points at U = $U_c$ and U = $U_s$ that separate the BI and MI phases for a given V. A charge-neutral spin-singlet exciton band develops in the BI phase (U<$U_c$) and drops below the band gap when U exceeds a special point Ue. The exciton gap closes at the first critical point $U_c$ while the charge and spin gaps persist and coincide between $U_c$ $U_s$) the charge gap increases almost linearly with U while the spin gap remains zero. These findings clarify earlier published results on the same model, and offer insights into several important issues regarding an appropriate scaling analysis of DMRG data and a full physical picture of the delicate nature of the phase transitions driven by electron correlation. The present work provides a comprehensive understanding for the critical behavior and phase diagram for the transition from BI to MI in one-dimensional correlated electron systems with a periodic alternating site potential.

cond-mat.str-el↗

arXiv2000

Superconducting correlations in ultra-small metallic grains

To describe the crossover from the bulk BCS superconductivity to a fluctuation-dominated regime in ultrasmall metallic grains, new order parameters and correlation functions, such as ``parity gap'' and ``pair-mixing correlation function'', have been recently introduced. In this paper, we discuss the small-grain behaviour of the Penrose-Onsager-Yang off-diagonal long-range order (ODLRO) parameter in a pseudo-spin representation. Relations between the ODLRO parameter and those mentioned above are established through analytical and numerical calculations.

cond-mat.supr-con↗

arXiv1998

Reaction-Diffusion-Branching Models of Stock Price Fluctuations

Several models of stock trading [P. Bak et al, Physica A {\bf 246}, 430 (1997)] are analyzed in analogy with one-dimensional, two-species reaction-diffusion-branching processes. Using heuristic and scaling arguments, we show that the short-time market price variation is subdiffusive with a Hurst exponent $H=1/4$. Biased diffusion towards the market price and blind-eyed copying lead to crossovers to the empirically observed random-walk behavior ($H=1/2$) at long times. The calculated crossover forms and diffusion constants are shown to agree well with simulation data.

cond-mat.stat-mech↗

arXiv1998

Parity effect in a small superconducting grain: A rigorous result

The parity effect in an ultra-small superconducting grain is examined. By applying a generalized version of Lieb's spin-reflection positivity technique, we show rigorously that the parity parameter $Δ_P$ is nonvanishing in such a system. A positive lower bound for $Δ_P$ is derived.

cond-mat.supr-con↗

arXiv1998

Charged and spin-excitation gaps in half-filled strongly correlated electron systems: A rigorous result

By exploiting the particle-hole symmetries of the Hubbard model, the periodic Anderson model and the Kondo lattice model at half-filling and applying a generalized version of Lieb's spin-reflection positivity method, we show that the charged gaps of these models are always larger than their spin excitation gaps. This theorem confirms the previous results derived by either the variational approach or the density renormalization group approach.

cond-mat.str-el↗