scholarly journals Topological phase transition in a generalized Kane-Mele-Hubbard model: A combined quantum Monte Carlo and Green's function study

2013 ◽  
Vol 87 (12) ◽  
Author(s):  
Hsiang-Hsuan Hung ◽  
Lei Wang ◽  
Zheng-Cheng Gu ◽  
Gregory A. Fiete
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Hubbard Model ◽  
Green’S Function ◽  
Green's Function ◽  
Quantum Monte Carlo ◽  
Topological Phase ◽  
Function Study ◽  
Topological Phase Transition

scholarly journals THE CHARACTERIZATION OF TOPOLOGICAL PROPERTIES IN QUANTUM MONTE CARLO SIMULATIONS OF THE KANE–MELE–HUBBARD MODEL

2013 ◽  
Vol 28 (01) ◽  
pp. 1430001 ◽  
Author(s):  
ZI YANG MENG ◽  
HSIANG-HSUAN HUNG ◽  
THOMAS C. LANG
Keyword(s):  
Monte Carlo ◽  
Hubbard Model ◽  
Green’S Function ◽  
Green's Function ◽  
Quantum Monte Carlo ◽  
Quantum Spin ◽  
Topological Phase ◽  
Correlation Effects ◽  
Topological Properties ◽  
Quantum Spin Hall

Topological insulators present a bulk gap, but allow for dissipationless spin transport along the edges. These exotic states are characterized by the Z2 topological invariant and are protected by time-reversal symmetry. The Kane–Mele model is one model to realize this topological class in two dimensions, also called the quantum spin Hall state. In this brief review article, we provide a pedagogical introduction to the influence of correlation effects in the quantum spin Hall states, with special focus on the half-filled Kane–Mele–Hubbard model, solved by means of unbiased determinant quantum Monte Carlo (QMC) simulations. We explain the idea of identifying the topological insulator via π-flux insertion, the Z2 invariant and the associated behavior of the zero-frequency Green's function, as well as the spin Chern number in parameter-driven topological phase transitions. The examples considered are two descendants of the Kane–Mele–Hubbard model, the generalized and dimerized Kane–Mele–Hubbard model. From the Z2 index, spin Chern numbers and the Green's function behavior, one can observe that correlation effects induce shifts of the topological phase boundaries. Although the implementation of these topological quantities has been successfully employed in QMC simulations to describe the topological phase transition, we also point out their limitations as well as suggest possible future directions in using numerical methods to characterize topological properties of strongly correlated condensed matter systems.

Green’s function of a 2D Fermi system undergoing a topological phase transition

JETP Letters ◽  
1999 ◽  
Vol 69 (2) ◽  
pp. 141-147 ◽  
Author(s):  
V. P. Gusynin ◽  
V. M. Loktev ◽  
S. G. Sharapov
Keyword(s):  
Phase Transition ◽  
Green’S Function ◽  
Green's Function ◽  
Fermi System ◽  
Topological Phase ◽  
Topological Phase Transition

scholarly journals Evidence of the Berezinskii-Kosterlitz-Thouless phase in a frustrated magnet

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Ze Hu ◽  
Zhen Ma ◽  
Yuan-Da Liao ◽  
Han Li ◽  
Chunsheng Ma ◽  
...  
Keyword(s):  
Phase Transition ◽  
Magnetic Materials ◽  
Quantum Monte Carlo ◽  
Topological Defects ◽  
Topological Phase ◽  
Topological Phase Transition ◽  
Out Of Plane ◽  
Frustrated Magnet ◽  
Experimental Findings ◽  
Quantum Monte Carlo Simulations

Abstract The Berezinskii-Kosterlitz-Thouless (BKT) mechanism, building upon proliferation of topological defects in 2D systems, is the first example of phase transition beyond the Landau-Ginzburg paradigm of symmetry breaking. Such a topological phase transition has long been sought yet undiscovered directly in magnetic materials. Here, we pin down two transitions that bound a BKT phase in an ideal 2D frustrated magnet TmMgGaO4, via nuclear magnetic resonance under in-plane magnetic fields, which do not disturb the low-energy electronic states and allow BKT fluctuations to be detected sensitively. Moreover, by applying out-of-plane fields, we find a critical scaling behavior of the magnetic susceptibility expected for the BKT transition. The experimental findings can be explained by quantum Monte Carlo simulations applied on an accurate triangular-lattice Ising model of the compound which hosts a BKT phase. These results provide a concrete example for the BKT phase and offer an ideal platform for future investigations on the BKT physics in magnetic materials.

scholarly journals Topological phase transition based on the attractive Hubbard model

2019 ◽  
Vol 127 (6) ◽  
pp. 67002
Author(s):  
Fenghua Qi ◽  
Jun Cao ◽  
Jie Cao ◽  
Xiao Li ◽  
Lifa Zhang
Keyword(s):  
Phase Transition ◽  
Hubbard Model ◽  
Topological Phase ◽  
Topological Phase Transition ◽  
Attractive Hubbard Model
Sign in / Sign up

Export Citation Format

Share Document