Jian-Hui Zhao

Publications (8)3.82 Total impact

• Source

  Available from: arxiv.org

  Article: Spontaneous symmetry breaking and bifurcations in ground-state fidelity for quantum lattice systems.

  Jian-Hui Zhao, Hong-Lei Wang, Bo Li, Huan-Qiang Zhou
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  ABSTRACT: Spontaneous symmetry breaking occurs in a system when its Hamiltonian possesses a certain symmetry, whereas the ground-state wave functions do not preserve it. This provides such a scenario that a bifurcation, which breaks the symmetry, occurs when some control parameter crosses its critical value. It is unveiled that the ground-state fidelity per lattice site exhibits such a bifurcation for quantum lattice systems undergoing quantum phase transitions. The significance of this result lies in the fact that the ground-state fidelity per lattice site is universal, in the sense that it is model independent, in contrast to (model-dependent) order parameters. This fundamental quantity may be computed by exploiting the developed tensor network algorithms on infinite-size lattices. We illustrate the scheme in terms of the quantum Ising model in a transverse magnetic field and the spin-1/2 XYX model in an external magnetic field on an infinite-size lattice in one spatial dimension.
  Physical Review E 12/2010; 82(6 Pt 1):061127. · 2.26 Impact Factor
• Article: Ground-state fidelity and entanglement entropy for the quantum three-state Potts model in one spatial dimension

  Yan-Wei Dai, Bing-Quan Hu, Jian-Hui Zhao, Huan-Qiang Zhou
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  ABSTRACT: The ground-state fidelity per lattice site is computed for the quantum three-state Potts model in a transverse magnetic field on an infinite-size lattice in one spatial dimension in terms of the infinite matrix product state algorithm. It is found that, on the one hand, a pinch point is identified on the fidelity surface around the critical point, and on the other hand, the ground-state fidelity per lattice site exhibits bifurcations at pseudo critical points for different values of the truncation dimension, which in turn approach the critical point as the truncation dimension becomes large. This implies that the ground-state fidelity per lattice site enables us to capture spontaneous symmetry breaking when the control parameter crosses the critical value. In addition, a finite-entanglement scaling of the von Neumann entropy is performed with respect to the truncation dimension, resulting in a precise determination of the central charge at the critical point. Finally, we compute the transverse magnetization, from which the critical exponent β is extracted from the numerical data.
  Journal of Physics A Mathematical and Theoretical 08/2010; 43(37):372001. · 1.56 Impact Factor
• Source

  Available from: ArXiv

  Article: Graded Projected Entangled-Pair State Representations and An Algorithm for Translationally Invariant Strongly Correlated Electronic Systems on Infinite-Size Lattices in Two Spatial Dimensions

  Qian-Qian Shi, Sheng-Hao Li, Jian-Hui Zhao, Huan-Qiang Zhou
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  ABSTRACT: An algorithm to find a graded Projected Entangled-Pair State representation of the ground state wave functions is developed for translationally invariant strongly correlated electronic systems on infinite-size lattices in two spatial dimensions. It is tested for the two-dimensional t-J model at and away from half filling, with truncation dimensions up to 6. We are able to locate a line of phase separation, which qualitatively agrees with the results based on the high-temperature expansions. We find that the model exhibits an extended s-wave superconductivity for J=0.4t at quarter filling. However, we emphasize that the currently accessible truncation dimensions are not large enough, so it is necessary to incorporate the symmetry of the system into the algorithm, in order to achieve results with higher precision. Comment: 5 pages, 5 figures
  07/2009;
• Source

  Available from: ArXiv

  Article: Quantum phase transitions and bifurcations: reduced fidelity as a phase transition indicator for quantum lattice many-body systems

  Jin-Hua Liu, Qian-Qian Shi, Jian-Hui Zhao, Huan-Qiang Zhou
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  ABSTRACT: We establish an intriguing connection between quantum phase transitions and bifurcations in the reduced fidelity between two different reduced density matrices for quantum lattice many-body systems with symmetry-breaking orders. Our finding is based on the observation that, in the conventional Landau-Ginzburg-Wilson paradigm, a quantum system undergoing a phase transition is characterized in terms of spontaneous symmetry breaking that is captured by a local order parameter, which in turn results in an essential change of the reduced density matrix in the symmetry-broken phase. Two quantum systems on an infinite lattice in one spatial dimension, i.e., quantum Ising model in a transverse magnetic field and quantum spin 1/2 XYX model in an external magnetic field, are considered in the context of the tensor network algorithm based on the matrix product state representation. Comment: 4+ pages, 4 figures
  05/2009;
• Source

  Available from: ArXiv

  Article: Kosterlitz-Thouless Phase Transition and Ground State Fidelity: a Novel Perspective from Matrix Product States

  Hong-Lei Wang, Jian-Hui Zhao, Bo Li, Huan-Qiang Zhou
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  ABSTRACT: The Kosterlitz-Thouless transition is studied from the representation of the systems's ground state wave functions in terms of Matrix Product States for a quantum system on an infinite-size lattice in one spatial dimension. It is found that, in the critical regime for a one-dimensional quantum lattice system with continuous symmetry, the newly-developed infinite Matrix Product State algorithm automatically leads to infinite degenerate ground states, due to the finiteness of the truncation dimension. This results in \textit{pseudo} continuous symmetry spontaneous breakdown, which allows to introduce a pseudo-order parameter that must be scaled down to zero, in order to be consistent with the Mermin-Wegner theorem. We also show that the ground state fidelity per lattice site exhibits a \textit{catastrophe point}, thus resolving a controversy regarding whether or not the ground state fidelity is able to detect the Kosterlitz-Thouless transition.
  03/2009;
• Source

  Available from: ArXiv

  Article: FAST TRACK COMMUNICATION: Fidelity approach to quantum phase transitions: finite-size scaling for the quantum Ising model in a transverse field

  Huan-Qiang Zhou, Jian-Hui Zhao, Bo Li
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  ABSTRACT: We analyze the fidelity per lattice site for two different ground states of the one-dimensional quantum Ising model in a transverse field near the critical point. It is found that, in the thermodynamic limit, the fidelity per lattice site is singular, and the derivative of its logarithmic function with respect to the transverse field strength is logarithmically divergent at the critical point. The scaling behavior is confirmed numerically by performing a finite-size scaling analysis for systems of different sizes, consistent with the conformal invariance at the critical point. This allows us to extract the correlation length critical exponent, which turns out to be universal in the sense that the correlation length critical exponent does not depend on either the anisotropic parameter or the transverse field strength.
  Journal of Physics A General Physics 11/2008; 41:2002.
• Source

  Available from: ArXiv

  Article: Singularities in ground state fidelity and quantum phase transitions for the Kitaev model

  Jian-Hui Zhao, Huan-Qiang Zhou
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  ABSTRACT: The ground state fidelity per lattice site is shown to be able to detect quantum phase transitions for the Kitaev model on the honeycomb lattice, a prototypical example of quantum lattice systems with topological order. It is found that, in the thermodynamic limit, the ground state fidelity per lattice site is non-analytic at the phase boundaries: the second-order derivative of its logarithmic function with respect to a control parameter describing the interaction between neighboring spins is logarithmically divergent. A finite size scaling analysis is performed, which allows us to extract the correlation length critical exponent from the scaling behaviors of the ground state fidelity per lattice site.
  04/2008;
• Source

  Available from: ArXiv

  Article: Singularities in fidelity surfaces for quantum phase transitions: a geometric perspective

  Huan-Qiang Zhou, Jian-Hui Zhao, Hong-Lei Wang, Bo Li
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  ABSTRACT: The fidelity per site between two ground states of a quantum lattice system corresponding to different values of the control parameter defines a surface embedded in a Euclidean space. The Gaussian curvature naturally quantifies quantum fluctuations that destroy orders at transition points. It turns out that quantum fluctuations wildly distort the fidelity surface near the transition points, at which the Gaussian curvature is singular in the thermodynamic limit. As a concrete example, the one-dimensional quantum Ising model in a transverse field is analyzed. We also perform a finite size scaling analysis for the transverse Ising model of finite sizes. The scaling behavior for the Gaussian curvature is numerically checked and the correlation length critical exponent is extracted, which is consistent with the conformal invariance at the critical point.
  12/2007;