# Excited-state quantum phase transitions in systems with two degrees of freedom: II. Finite-size effects

## Abstract

This article extends our previous analysis Stránský et al. (2014) of Excited-State Quantum Phase Transitions (ESQPTs) in systems of dimension two. We focus on the oscillatory component of the quantum state density in connection with ESQPT structures accompanying a first-order ground-state transition. It is shown that a separable (integrable) system can develop rather strong finite-size precursors of ESQPT expressed as singularities in the oscillatory component of the state density. The singularities originate in effectively 1-dimensional dynamics and in some cases appear in multiple replicas with increasing excitation energy. Using a specific model example, we demonstrate that these precursors are rather resistant to proliferation of chaotic dynamics. - Highlights: • Oscillatory components of state density and spectral flow studied near ESQPTs. • Enhanced finite-size precursors of ESQPT caused by fully/partly separable dynamics. • These precursors appear due to criticality of a subsystem with lower dimension. • Separability-induced finite-size effects disappear in case of fully chaotic dynamics.

- Authors:

- Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 18000 Prague (Czech Republic)
- (United States)
- Racah Institute of Physics, The Hebrew University, 91904 Jerusalem (Israel)

- Publication Date:

- OSTI Identifier:
- 22451163

- Resource Type:
- Journal Article

- Journal Name:
- Annals of Physics

- Additional Journal Information:
- Journal Volume: 356; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHAOS THEORY; DEGREES OF FREEDOM; EXCITED STATES; GROUND STATES; ONE-DIMENSIONAL CALCULATIONS; PHASE TRANSFORMATIONS; QUANTUM STATES

### Citation Formats

```
Stránský, Pavel, Macek, Michal, Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, CT 06520-8120, Leviatan, Amiram, and Cejnar, Pavel, E-mail: pavel.cejnar@mff.cuni.cz.
```*Excited-state quantum phase transitions in systems with two degrees of freedom: II. Finite-size effects*. United States: N. p., 2015.
Web. doi:10.1016/J.AOP.2015.02.025.

```
Stránský, Pavel, Macek, Michal, Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, CT 06520-8120, Leviatan, Amiram, & Cejnar, Pavel, E-mail: pavel.cejnar@mff.cuni.cz.
```*Excited-state quantum phase transitions in systems with two degrees of freedom: II. Finite-size effects*. United States. doi:10.1016/J.AOP.2015.02.025.

```
Stránský, Pavel, Macek, Michal, Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, CT 06520-8120, Leviatan, Amiram, and Cejnar, Pavel, E-mail: pavel.cejnar@mff.cuni.cz. Fri .
"Excited-state quantum phase transitions in systems with two degrees of freedom: II. Finite-size effects". United States. doi:10.1016/J.AOP.2015.02.025.
```

```
@article{osti_22451163,
```

title = {Excited-state quantum phase transitions in systems with two degrees of freedom: II. Finite-size effects},

author = {Stránský, Pavel and Macek, Michal and Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, CT 06520-8120 and Leviatan, Amiram and Cejnar, Pavel, E-mail: pavel.cejnar@mff.cuni.cz},

abstractNote = {This article extends our previous analysis Stránský et al. (2014) of Excited-State Quantum Phase Transitions (ESQPTs) in systems of dimension two. We focus on the oscillatory component of the quantum state density in connection with ESQPT structures accompanying a first-order ground-state transition. It is shown that a separable (integrable) system can develop rather strong finite-size precursors of ESQPT expressed as singularities in the oscillatory component of the state density. The singularities originate in effectively 1-dimensional dynamics and in some cases appear in multiple replicas with increasing excitation energy. Using a specific model example, we demonstrate that these precursors are rather resistant to proliferation of chaotic dynamics. - Highlights: • Oscillatory components of state density and spectral flow studied near ESQPTs. • Enhanced finite-size precursors of ESQPT caused by fully/partly separable dynamics. • These precursors appear due to criticality of a subsystem with lower dimension. • Separability-induced finite-size effects disappear in case of fully chaotic dynamics.},

doi = {10.1016/J.AOP.2015.02.025},

journal = {Annals of Physics},

issn = {0003-4916},

number = ,

volume = 356,

place = {United States},

year = {2015},

month = {5}

}