# Quenches on thermofield double states and time reversal symmetry

## Abstract

In this paper we study a quench protocol on thermofield double states in the presence of time-reversal symmetry that is inspired by the work of Gao et al. The deformation is a product of Hermitian operators on the left and right systems that are identical to each other and that lasts for a small amount of time. We study the linear dependence on the quench to the properties of the deformation under time reversal. If the quench is time symmetric, then the linear response after the quench of all T-even operators vanishes. This includes the response of the energy on the left system and all the thermodynamic expectation values (the time averaged expectation values of the operators). Also, we show under an assumption of nondegeneracy of the Hamiltonian that the entanglement entropy between left and right is not affected to this order. We also study a variation of the quench where an instantaneous deformation is given by an operator of fixed T-parity and its time derivative. It is shown that the sign of the response of the Hamiltonian is correlated with the T-parity of the operator. We can then choose the sign of the amplitude of the quench to resultmore »

- Authors:

- Publication Date:

- Research Org.:
- Univ. of California, Santa Barbara, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1615034

- Alternate Identifier(s):
- OSTI ID: 1657857

- Grant/Contract Number:
- SC0019139

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 6; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Quantum quench; Gauge/gravity duality; Quantum aspects of black holes.

### Citation Formats

```
Berenstein, David. Quenches on thermofield double states and time reversal symmetry. United States: N. p., 2019.
Web. https://doi.org/10.1103/PhysRevD.100.066022.
```

```
Berenstein, David. Quenches on thermofield double states and time reversal symmetry. United States. https://doi.org/10.1103/PhysRevD.100.066022
```

```
Berenstein, David. Mon .
"Quenches on thermofield double states and time reversal symmetry". United States. https://doi.org/10.1103/PhysRevD.100.066022.
```

```
@article{osti_1615034,
```

title = {Quenches on thermofield double states and time reversal symmetry},

author = {Berenstein, David},

abstractNote = {In this paper we study a quench protocol on thermofield double states in the presence of time-reversal symmetry that is inspired by the work of Gao et al. The deformation is a product of Hermitian operators on the left and right systems that are identical to each other and that lasts for a small amount of time. We study the linear dependence on the quench to the properties of the deformation under time reversal. If the quench is time symmetric, then the linear response after the quench of all T-even operators vanishes. This includes the response of the energy on the left system and all the thermodynamic expectation values (the time averaged expectation values of the operators). Also, we show under an assumption of nondegeneracy of the Hamiltonian that the entanglement entropy between left and right is not affected to this order. We also study a variation of the quench where an instantaneous deformation is given by an operator of fixed T-parity and its time derivative. It is shown that the sign of the response of the Hamiltonian is correlated with the T-parity of the operator. We can then choose the sign of the amplitude of the quench to result in a reduction in the energy. This implies a reduction of the entanglement entropy between both sides.},

doi = {10.1103/PhysRevD.100.066022},

journal = {Physical Review D},

number = 6,

volume = 100,

place = {United States},

year = {2019},

month = {9}

}

https://doi.org/10.1103/PhysRevD.100.066022

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