Shi-Jian Gu

Entanglement and Quantum Phase Transition in the Extended Hubbard Model

We study quantum entanglement in a one-dimensional correlated fermionic system. Our results show, for the first time, that entanglement can be used to identify quantum phase transitions in fermionic systems.

FIDELITY APPROACH TO QUANTUM PHASE TRANSITIONS

We review the quantum fidelity approach to quantum phase transitions in a pedagogical manner. We try to relate all established but scattered results on the leading term of the fidelity into a systematic theoretical framework, which might provide an alternative paradigm for understanding quantum critical phenomena. The definition of the fidelity and the scaling behavior of its leading term, as well as their explicit applications to the one-dimensional transverse-field Ising model and the Lipkin–Meshkov–Glick model, are introduced at the graduate-student level. Besides, we survey also other types of fidelity approach, such as the fidelity per site, reduced fidelity, thermal-state fidelity, operator fidelity, etc; as well as relevant works on the fidelity approach to quantum phase transitions occurring in various many-body systems.

Fidelity, dynamic structure factor, and susceptibility in critical phenomena

Motivated by the growing importance of fidelity in quantum critical phenomena, we establish a general relation between the fidelity and structure factor of the driving term in a Hamiltonian through the concept of fidelity susceptibility. Our discovery, as shown by some examples, facilitates the evaluation of fidelity in terms of susceptibility using well-developed techniques, such as density matrix renormalization group for the ground state, or Monte Carlo simulations for the states in thermal equilibrium.

Entanglement, quantum phase transition, and scaling in the XXZ chain

Motivated by recent development in quantum entanglement, we study relations among concurrence C, SU{sub q}(2) algebra, quantum phase transition and correlation length at the zero temperature for the XXZ chain. We find that at the SU(2) point, the ground state possesses the maximum concurrence. When the anisotropic parameter {delta} is deformed, however, its value decreases. Its dependence on {delta} scales as C=C{sub 0}-C{sub 1}({delta}-1){sup 2} in the XY metallic phase and near the critical point (i.e., 1<{delta}<1.3) of the Ising-like insulating phase. We also study the dependence of C on the correlation length {xi}, and show that it satisfies C=C{sub 0}-1/2{xi} near the critical point. For different sizes of the system, we show that there exists a universal scaling function of C with respect to the correlation length {xi}.

Fidelity susceptibility, scaling, and universality in quantum critical phenomena

We study fidelity susceptibility in the one-dimensional asymmetric Hubbard model and show that the fidelity susceptibility can be used to identify the universality class of the quantum phase transitions in this model. The Kosterlitz\char21{}Thouless-type transition occurred at half-filling and the Landau transition away from half-filling can be discriminated from distinct critical exponents of the fidelity susceptibility.

Universal role of correlation entropy in critical phenomena

In statistical physics, if we divide successively an equilibrium system into two parts, we will face a situation that, to a certain length., the physics of a subsystem is no longer the same as the original one. The extensive property of the thermal entropy S(A boolean OR B) = S(A) + S(B) is then violated. This observation motivates us to introduce a concept of correlation entropy between two points, as measured by the mutual information in information theory, to study the critical phenomena. A rigorous relation is established to display some drastic features of the non-vanishing correlation entropy of a subsystem formed by any two distant particles with long-range correlation. This relation actually indicates a universal role played by the correlation entropy for understanding the critical phenomena. We also verify these analytical studies in terms of two well-studied models for both the thermal and quantum phase transitions: the two-dimensional Ising model and the one-dimensional transverse-field Ising model. Therefore, the correlation entropy provides us with a new physical intuition of the critical phenomena from the point of view of information theory.

Entanglement of the heisenberg chain with the next-nearest-neighbor interaction

The features of the concurrences between the nearest-neighbors and that of the next-nearest-neighbors for the one-dimensional Heisenberg model with next-nearest-neighbor coupling J are studied as functions of temperature and J. The two concurrences exhibit a different dependence on J at the ground state, which could be interpreted from the point of view of the correlation functions. The threshold temperature at which the concurrence is zero and the temperature effect on the two concurrences for systems up to 12 sites are studied numerically.

Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model

We study exactly both the ground-state fidelity susceptibility and bond-bond correlation function in the Kitaev honeycomb model. Our results show that the fidelity susceptibility can be used to identify the topological phase transition from a gapped A phase with Abelian anyon excitations to a gapless B phase with non-Abelian anyon excitations. We also find that the bond-bond correlation function decays exponentially in the gapped phase, but algebraically in the gapless phase. For the former case, the correlation length is found to be 1/xi=2 sinh(-1)[root 2J(z)-1/(1-J(z))], which diverges around the critical point J(z)=(1/2)(+).

Fidelity and quantum phase transition for the Heisenberg chain with next-nearest-neighbor interaction.

In this paper, we investigate the fidelity for the Heisenberg chain with the next-nearest-neighbor interaction (or the J1-J2 model) and analyze its connections with quantum phase transition. We compute the fidelity between the ground states and find that the phase transition point of the J1-J2 model cannot be well characterized by the ground-state fidelity for finite-size systems. Instead, we introduce and calculate the fidelity between the first excited states. Our results show that the quantum transition can be well characterized by the fidelity of the first excited state even for a small-size system.

Local entanglement and quantum phase transition in spin models

In this paper, we study quantum phase transitions in both the one- and two-dimensional XXZ models with either spin S = 1/2 or S = 1 by a local entanglement Ev. We show that the behaviour of Ev is dictated by the low-lying spin excitation spectra of these systems. Therefore, the anomalies of Ev imply their critical points. This recalls the well-known fact in optics: the three-dimensional image of one subject can be recovered from a small piece of holograph, which records the interference pattern of the reflected light beams from it. Similarly, we find that the local entanglement, which is rooted in the quantum superposition principle, provides us with a deep insight into the long-range spin correlations in these quantum spin systems.