Static vs. dynamic phases of quantum many-body systems

We review the effects of excited-state quantum phase transitions (ESQPTs) in interacting many-body systems with finite numbers of collective degrees of freedom. We classify typical ESQPT signatures in the spectra of energy eigenstates with respect to the underlying classical dynamics and outline a variety of quantum systems in which they occur. We describe thermodynamic and dynamic consequences of ESQPTs, like those in microcanonical thermodynamics, quantum quench dynamics, and in the response to nearly adiabatic or periodic driving. We hint at some generalizations of the ESQPT concept in periodic lattices and in resonant tunneling systems.

show abstract

“…Vertical lines mark the ESQPT critical energies (the same as in figure 1). Adapted from reference [141].…”

Section: Singularities In the Spectra Of Excited Statesmentioning

confidence: 99%

“…Acronyms D, TC, N and S mark quantum phases of the model. Adapted from[141], with the permission of AIP Publishing.…”

mentioning

confidence: 99%

Excited-state quantum phase transitions

Cejnar

Stránský

Macek

et al. 2021

J. Phys. A: Math. Theor.

Self Cite

127

View full text Add to dashboard Cite

show abstract

“…ESQPTs are currently studied in diverse systems including atomic nuclei, molecules, coupled atom-field quantum optics systems, driven quantum oscillators, and also two dimensional lattices, with seminal inputs in most of these fields by Franco Iachello. The interest in ESQPTs stems on one hand from the marked structural changes occurring in the individual systems, on the other hand from possible profound general implications for non-equilibrium thermodynamics, quantum information processing, and transport (for a review see [4]). A general classification of the ESQPTs is based on the dimensionality (number of degrees of freedom) of the system and the types of stationary points of the underlying semi-classical energy manifold, see Refs.…”

mentioning

confidence: 99%

Van Hove singularities and excited-state quantum phase transitions in graphene-like microwave billiards

Macek

Dietz

2019

AIP Conference Proceedings

Self Cite

View full text Add to dashboard Cite

We discuss solutions of an algebraic model of the hexagonal lattice vibrations, which point out interesting localization properties of the eigenstates at van Hove singularities (vHs), whose energies correspond to Excited-State Quantum Phase Transitions (ESQPT). We show that these states form stripes oriented parallel to the zig-zag direction of the lattice, similar to the well-known edge states found at the Dirac point, however the vHs-stripes appear in the bulk. We interpret the states as lines of cell-tilting vibrations, and inspect their stability in the large lattice-size limit. The model can be experimentally realized by superconducting 2D microwave resonators containing triangular lattices of metallic cylinders, which simulate finite-sized graphene flakes. Thus we can assume that the effects discussed here could be experimentally observed.

show abstract

Excited-state quantum phase transitions in bosonic lattice systems

Macek¹

2019

AIP Conference Proceedings

Self Cite

View full text Add to dashboard Cite

Concentrating on bosonic lattice systems, we ask whether and how Excited State Quantum Phase Transition (ESQPT) singularities occur in condensed matter systems with ground state QPTs. We study in particular the spectral singularities above the ground-state phase diagram of the boson Hubbard model. As a general prerequisite, we point out the analogy between ESQPTs and van Hove singularities (vHss). arXiv:1901.09677v2 [cond-mat.mes-hall]

show abstract

Static vs. dynamic phases of quantum many-body systems

Cited by 4 publications

References 59 publications

Excited-state quantum phase transitions

Excited-state quantum phase transitions

Van Hove singularities and excited-state quantum phase transitions in graphene-like microwave billiards

Excited-state quantum phase transitions in bosonic lattice systems

Contact Info

Product

Resources

About