scholarly journals Anomalies and renormalization of mixed states in quantum theories

2014 ◽  
Vol 29 (13) ◽  
pp. 1450064 ◽  
Author(s):  
Kumar S. Gupta ◽  
Amilcar de Queiroz
Keyword(s):  
Moduli Space ◽  
Time Reversal ◽  
Condensed Matter ◽  
Quantum Spin ◽  
Hamiltonian Approach ◽  
Mixed States ◽  
Expectation Values ◽  
Quantum Theories ◽  
Long Wavelength ◽  
Mass Gap

In a Hamiltonian approach to anomalies, parity and time-reversal symmetries can be restored by introducing suitable impure (or mixed) states. However, the expectation values of observables such as the Hamiltonian diverges in such impure states. Here, we show that such divergent expectation values can be treated within a renormalization group (RG) framework, leading to a set of β-functions in the moduli space of the operators representing the observables. This leads to well-defined expectation values of the Hamiltonian in a phase where the impure state restores the P and T symmetry. We also show that this RG procedure leads to a mass gap in the spectrum. Such a framework may be relevant for long wavelength descriptions of condensed matter systems such as the quantum spin Hall (QSH) effect.

scholarly journals Voltage-tunable Majorana bound states in time-reversal symmetric bilayer quantum spin Hall hybrid systems

2019 ◽  
Vol 100 (16) ◽  
Author(s):  
F. Schulz ◽  
J. C. Budich ◽  
E. G. Novik ◽  
P. Recher ◽  
B. Trauzettel
Keyword(s):  
Hybrid Systems ◽  
Time Reversal ◽  
Bound States ◽  
Quantum Spin ◽  
Majorana Bound States ◽  
Quantum Spin Hall

scholarly journals q-DEFORMATIONS OF QUANTUM SPIN CHAINS WITH EXACT VALENCE-BOND GROUND STATES

1994 ◽  
Vol 08 (25n26) ◽  
pp. 3645-3654 ◽  
Author(s):  
M.T. BATCHELOR ◽  
C.M. YUNG
Keyword(s):  
Condensed Matter ◽  
Valence Bond ◽  
Ground States ◽  
Quantum Spin ◽  
Total Spin ◽  
Spin Chains ◽  
The Other ◽  
Condensed Matter Physics ◽  
Spin States ◽  
Quantum Spin Chains

Quantum spin chains with exact valence-bond ground states are of great interest in condensed-matter physics. A class of such models was proposed by Affleck et al., each of which is su(2)-invariant and constructed as a sum of projectors onto definite total spin states at neighboring sites. We propose to use the machinery of the q-deformation of su(2) to obtain generalisations of such models, and work out explicitly the two simplest examples. In one case we recover the known anisotropic spin-1 VBS model while in the other we obtain a new anisotropic generalisation of the spin-½ Majumdar-Ghosh model.

scholarly journals Stochastic locality and master-field simulations of very large lattices

2018 ◽  
Vol 175 ◽  
pp. 01002 ◽  
Author(s):  
Martin Lüscher
Keyword(s):  
Gauge Theory ◽  
Lattice Qcd ◽  
Field Theories ◽  
Expectation Values ◽  
Mass Gap ◽  
Large Lattice ◽  
Technical Issues ◽  
The Subject ◽  
Local Observables

In lattice QCD and other field theories with a mass gap, the field variables in distant regions of a physically large lattice are only weakly correlated. Accurate stochastic estimates of the expectation values of local observables may therefore be obtained from a single representative field. Such master-field simulations potentially allow very large lattices to be simulated, but require various conceptual and technical issues to be addressed. In this talk, an introduction to the subject is provided and some encouraging results of master-field simulations of the SU(3) gauge theory are reported.

scholarly journals Geometric phases for mixed states of the Kitaev chain

2016 ◽  
Vol 374 (2068) ◽  
pp. 20150231 ◽  
Author(s):  
Ole Andersson ◽  
Ingemar Bengtsson ◽  
Marie Ericsson ◽  
Erik Sjöqvist
Keyword(s):  
Finite Temperature ◽  
Geometric Phase ◽  
Berry Phase ◽  
Condensed Matter ◽  
Order Parameters ◽  
Topological Order ◽  
Mixed States ◽  
Geometric Phases

The Berry phase has found applications in building topological order parameters for certain condensed matter systems. The question whether some geometric phase for mixed states can serve the same purpose has been raised, and proposals are on the table. We analyse the intricate behaviour of Uhlmann's geometric phase in the Kitaev chain at finite temperature, and then argue that it captures quite different physics from that intended. We also analyse the behaviour of a geometric phase introduced in the context of interferometry. For the Kitaev chain, this phase closely mirrors that of the Berry phase, and we argue that it merits further investigation.

Time-reversal symmetry protected chiral interface states between quantum spin and quantum anomalous Hall insulators

2015 ◽  
Vol 92 (7) ◽  
Author(s):  
Huaqing Huang ◽  
Zhaoyou Wang ◽  
Nannan Luo ◽  
Zhirong Liu ◽  
Rong Lü ◽  
...  
Keyword(s):  
Time Reversal ◽  
Interface States ◽  
Quantum Spin ◽  
Time Reversal Symmetry ◽  
Symmetry Protected

Quantum spin Hall state in cyanided dumbbell stanene

RSC Advances ◽  
2016 ◽  
Vol 6 (89) ◽  
pp. 86089-86094 ◽  
Author(s):  
Min Yuan ◽  
Wei-xiao Ji ◽  
Miao-juan Ren ◽  
Ya-ping Wang ◽  
Hui Zhao
Keyword(s):  
High Temperature ◽  
Hall Effect ◽  
Band Gap ◽  
Condensed Matter ◽  
Quantum Spin ◽  
Condensed Matter Physics ◽  
Two Dimensional ◽  
Important Goal ◽  
Quantum Spin Hall Effect ◽  
Quantum Spin Hall

Searching for two-dimensional (2D) quantum spin Hall (QSH) insulators with a large band gap, in which the Quantum spin Hall effect (QSHE) can be observed at high temperature, is an important goal for condensed matter physics researchers.

ONE AND QUASI-ONE DIMENSIONAL SPIN SYSTEMS

2003 ◽  
Vol 18 (33n35) ◽  
pp. 2329-2336 ◽  
Author(s):  
Elisa Ercolessi
Keyword(s):  
Condensed Matter ◽  
Quantum Spin ◽  
Spin Systems ◽  
Spin Chains ◽  
Famous Conjecture ◽  
One Dimensional ◽  
Conformal Field ◽  
Quantum Spin Models ◽  
Low Dimensional ◽  
Antiferromagnetic Spin

Quantum spin models represent one of the most studied examples of application of low-dimensional field theories to condensed matter systems. In this paper we will review some chapters of this hystory, that dates back to the early '80, when Haldane put forward his by now famous conjecture on antiferromagnetic spin chains, and reaches the present days, with the most advanced applications of integrable models and conformal field theory.

scholarly journals Lattice Hamiltonian approach to the massless Schwinger model: Precise extraction of the mass gap

2013 ◽  
Vol 184 (7) ◽  
pp. 1666-1672 ◽  
Author(s):  
Krzysztof Cichy ◽  
Agnieszka Kujawa-Cichy ◽  
Marcin Szyniszewski
Keyword(s):  
Hamiltonian Approach ◽  
Schwinger Model ◽  
Mass Gap

scholarly journals Time-reversal-breaking induced quantum spin Hall effect

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
Wei Luo ◽  
D. X. Shao ◽  
Ming-Xun Deng ◽  
W. Y. Deng ◽  
L. Sheng
Keyword(s):  
Hall Effect ◽  
Time Reversal ◽  
Quantum Spin ◽  
Spin Hall Effect ◽  
Quantum Spin Hall Effect ◽  
Quantum Spin Hall
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