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

Pavel Stránský; Michal Macek; Amiram Leviatan; Pavel Cejnar

doi:10.1016/j.aop.2015.02.025

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

Pavel Stránský, Michal Macek, Amiram Leviatan, Pavel Cejnar^*

^*Corresponding author for this work

Racah Institute of Physics

Research output: Contribution to journal › Article › peer-review

54 Scopus citations

Abstract

This article extends our previous analysis Stránský etal. (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.

Original language	American English
Pages (from-to)	57-82
Number of pages	26
Journal	Annals of Physics
Volume	356
DOIs	https://doi.org/10.1016/j.aop.2015.02.025
State	Published - 1 May 2015

Bibliographical note

Funding Information:
This work was performed under the project no. P203-13-07117S of the Czech Science Foundation. P.S. acknowledges support by CONACyT and PAPIIT-UNAM, Mexico . A.L. and M.M. appreciate the funding by Israel Science Foundation and the Golda Meir Fellowship .

Publisher Copyright:
© 2015.

Keywords

Finite-size effects
Oscillatory component of level density
Quantum phase transitions
Regular/chaotic dynamics

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10.1016/j.aop.2015.02.025

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abstract = "This article extends our previous analysis Str{\'a}nsk{\'y} etal. (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.",

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AU - Macek, Michal

AU - Leviatan, Amiram

AU - Cejnar, Pavel

N1 - Funding Information: This work was performed under the project no. P203-13-07117S of the Czech Science Foundation. P.S. acknowledges support by CONACyT and PAPIIT-UNAM, Mexico . A.L. and M.M. appreciate the funding by Israel Science Foundation and the Golda Meir Fellowship . Publisher Copyright: © 2015.

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N2 - This article extends our previous analysis Stránský etal. (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.

AB - This article extends our previous analysis Stránský etal. (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.

KW - Finite-size effects

KW - Oscillatory component of level density

KW - Quantum phase transitions

KW - Regular/chaotic dynamics

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EP - 82

JO - Annals of Physics

JF - Annals of Physics

ER -

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

Abstract

Bibliographical note

Keywords

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