Qian-Qian Shi

Finite-size geometric entanglement from tensor network algorithms

The global geometric entanglement (GE) is studied in the context of newly developed tensor network algorithms for finite systems. For one-dimensional quantum spin systems it is found that, at criticality, the leading finite-size correction to the global GE per site behaves as b/n, where n is the size of the system and b a given coefficient. Our conclusion is based on the computation of the GE per spin for the quantum Ising model in a transverse magnetic field and for the spin-1/2 XXZ model. We also discuss the possibility of coefficient b being universal.

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

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 order. 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. a quantum Ising model in a transverse magnetic field and a 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.

Geometric entanglement and quantum phase transitions in two-dimensional quantum lattice models

Geometric entanglement (GE), as a measure of multipartite entanglement, has been investigated as a universal tool to detect phase transitions in quantum many-body lattice models. In this paper we outline a systematic method to compute GE for two-dimensional (2D) quantum many-body lattice models based on the translational invariant structure of infinite projected entangled pair state (iPEPS) representations. By employing this method, the

Universal Order Parameters and Quantum Phase Transitions: A Finite-Size Approach

q

Groundstate fidelity phase diagram of the fully anisotropic two-leg spin-½ XXZ ladder

-state quantum Potts model on the square lattice with

Tensor network states and ground-state fidelity for quantum spin ladders

q\ensuremath{\in}{2,3,4,5}

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

is investigated as a prototypical example. Further, we have explored three 2D Heisenberg models: the antiferromagnetic spin-1/2

Universal construction of order parameters for translation-invariant quantum lattice systems with symmetry-breaking order.

XXX

Geometric entanglement for quantum critical spin chains belonging to the Ising and three-state Potts universality classes

and anisotropic

Duality and ground-state phase diagram for the quantum XYZ model with arbitrary spin

XYX