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Finite-temperature topological entanglement entropy for CSS codes

Zhi Li, Roger S. K. Mong

We consider topological entanglement entropy (TEE) at finite temperature for CSS codes, which include some ordinary topological-ordered systems such as the toric code and some fracton models such as the Haah's code and the X-cube model. We find, under the assumption that there is no extended critical phase, the finite-temperature TEE is a piecewise constant function of the temperature, with possible discontinuities only at phase transitions. We then consider phase transitions of CSS codes. We claim that there must exist a phase transition at zero temperature for any CSS codes in 2D and 3D with topological order. This statement can be rigorous proved for some familiar examples, while for general models it can be argued based on the low-temperature expansion. This indicates the break down of topological orders at finite temperature. We also discuss possible connections with self-correcting quantum memory.We consider topological entanglement entropy (TEE) at finite temperature for CSS codes, which include some ordinary topological-ordered systems such as the toric code and some fracton models such as the Haah's code and the X-cube model. We find, under the assumption that there is no extended critical phase, the finite-temperature TEE is a piecewise constant function of the temperature, with possible discontinuities only at phase transitions. We then consider phase transitions of CSS codes. We claim that there must exist a phase transition at zero temperature for any CSS codes in 2D and 3D with topological order. This statement can be rigorous proved for some familiar examples, while for general models it can be argued based on the low-temperature expansion. This indicates the break down of topological orders at finite temperature. We also discuss possible connections with self-correcting quantum memory.

arXiv:1910.07545Oct 16, 20194 citations

“Phase transitions” at finite temperature in finite systems

E. D. D. Davis, H. G. Miller

Physics Letters BOct 1, 198726 citations

Phase Transitions in the Generalized XY Model at f = 1/2

Beom Jun Kim, Petter Minnhagen, Sebastian Bernhardsson

Journal of the Korean Physical SocietyAug 14, 20080 citations

Fracton topological order at finite temperature

Xiaoyang Shen, Zhengzhi Wu, Linhao Li +2 more

This article reports on a finite temperature phase transition in the four-dimensional X-cube model. The authors have proposed the low temperature phase spontaneously breaks the 1-form subsystem symmetry.

arXiv:2109.06887Physical Review ResearchJul 13, 202223 citations

The xy model for phase transitions: some static and dynamic properties

R.V. Ditzian

Jan 1, 19700 citations

The absence of finite-temperature phase transitions in low-dimensional many-body models: a survey and new results

Axel Gelfert, Wolfgang Nolting

After a brief discussion of the Bogoliubov inequality and possible generalizations thereof, we present a complete review of results concerning the Mermin-Wagner theorem for various many-body systems, geometries and order parameters. We extend the method to cover magnetic phase transitions in the periodic Anderson model as well as certain superconducting pairing mechanisms for Hubbard films. The relevance of the Mermin-Wagner theorem to approximations in many-body physics is discussed on a conceptual level.After a brief discussion of the Bogoliubov inequality and possible generalizations thereof, we present a complete review of results concerning the Mermin-Wagner theorem for various many-body systems, geometries and order parameters. We extend the method to cover magnetic phase transitions in the periodic Anderson model as well as certain superconducting pairing mechanisms for Hubbard films. The relevance of the Mermin-Wagner theorem to approximations in many-body physics is discussed on a conceptual level.

arXiv:cond-mat/0106090Journal of Physics Condensed MatterJun 25, 200169 citations

Absence of finite temperature phase transitions in the X-Cube model and its Z p generalization

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