Signatures of excited-state quantum phase transitions in quantum many-body systems: Phase space analysis

Wang, Qian; Pérez‐Bernal, F.

doi:10.1103/physreve.104.034119

Cited by 23 publications

(18 citation statements)

References 120 publications

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“…And third, the broken-symmetry phase at > extends up to a certain critical energy, , at which an ESQPT takes place; below this energy, the spectrum is composed by parity doublets exactly degenerate in the TL [29,36]. As typical examples, we quote the Lipkin-Meshkov-Glick (LMG) model [38][39][40][41][42][43][44][45][46], the Dicke and Rabi models [47][48][49][50][51][52][53][54], spinor Bose-Einstein condensates [55], the coupled top [56] and the two-site Bose-Hubbard model [57].…”

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confidence: 99%

Theory of dynamical phase transitions in quantum systems with symmetry-breaking eigenstates

Corps¹,

Relaño²

2022

Preprint

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We present a theory for the two kinds of dynamical quantum phase transitions, sometimes termed DPT-I and DPT-II, in collective many-body systems. Both are triggered by excited-state quantum phase transitions. For quenches below the critical energy, the existence of an additional conserved charge, identifying the corresponding phase, allows for a non-zero value of the dynamical order parameter characterizing DPTs-I, and precludes the mechanism giving rise to non-analyticities in the return probability, trademark of DPTs-II. We propose a statistical ensemble describing the long-time averages of order parameters in DPTs-I, and provide a theoretical proof for the absence of true DPT-II critical times in the thermodynamic limit in the phase with this additional conserved charge. Our results are numerically illustrated in the fully-connected transverse-field Ising model, which exhibits both kinds of dynamical phase transitions.

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confidence: 99%

Theory of dynamical phase transitions in quantum systems with symmetry-breaking eigenstates

Corps¹,

Relaño²

2022

Preprint

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“…In this case, V (x) = V (−x), and therefore Eq. ( 1) is a toy model for one degree of freedom systems with a Z 2 symmetry, like the Lipkin-Meshkov-Glick and the two-fluid Lipkin model, the two-site Bose-Hubbard, the coupled top, and the Dicke and the Rabi models [17,[20][21][22]32,34,[48][49][50][51][52][53][54][55][56]. If b 0, the single critical point is x c1 = 0, whereas if b 0 there appears a second pair of critical points, x c2, 3 the QPT and the emergence of the critical ESQPT.…”

Section: Classical Toy Modelmentioning

confidence: 99%

Energy cat states induced by a parity-breaking excited-state quantum phase transition

Corps

Relaño

2022

Phys. Rev. A

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We show that excited-state quantum phase transitions (ESQPTs) in a system in which the parity symmetry is broken can be used to engineer an energy cat state-a Schrödinger cat state involving a quantum superposition of both different positions and energies. By means of a generalization of the Rabi model, we show that adding a parity-breaking term annihilates the ground-state quantum phase transition between normal and superradiant phases, and induces the formation of three excited-state phases, all of them identified by means of an observable with two eigenvalues. In one of these phases, level crossings are observed in the thermodynamic limit. These allow us to separate a wave function into two parts: one, with lower energy, trapped within one region of the spectrum, and a second one, with higher energy, trapped within another. Finally, we show that a generalized microcanonical ensemble, including two different average energies, is required to properly describe equilibrium states in this situation. Our results illustrate yet another physical consequence of ESQPTs.

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“…Although all numerical results in this paper concern the fully-connected transverse-field Ising model, our theory is applicable to a broad class of collective quantum systems; as paradigmatic examples, we highlight the Lipkin-Meshkov-Glick model (LMG) model (a version of which is mathematically equivalent to the fully-connected transverse-field Ising model) [45][46][47][48][49][50][51][52][53], the Rabi and Dicke models [54][55][56][57][58][59][60][61][62][63][64], the coupled top [65], spinor Bose-Einstein condensates [66], or the two-site Bose-Hubbard Hamiltonian [67], to cite a few.…”

Section: Generic Setupmentioning

confidence: 99%

Dynamical and excited-state quantum phase transitions in collective systems

Corps,

Relaño

2022

Preprint

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We study dynamical phase transitions (DPTs) in quantum many-body systems with infinite-range interaction, and present a theory connecting the two kinds of known DPTs (sometimes referred to as DPTs-I and DPTs-II) with the concept of excited-state quantum phase transition (ESQPT), traditionally found in collective models. We show that DPTs-I appear as a manifestation of symmetry restoration after a quench from the broken-symmetry phase, the limits between these two phases being demarcated precisely by an ESQPT. We describe the order parameters of DPTs-I with a generalization of the standard microcanonical ensemble incorporating the information of an additional conserved charge identifying the corresponding phase. We also show that DPTs-I are linked to a mechanism of information erasure brought about by the ESQPT, and quantify this information loss with the statistical ensemble that we propose. Finally, we show analytically that DPTs-II are forbidden in these systems for quenches leading a broken-symmetry initial state to the same broken-symmetry phase, on one side of the ESQPT, and we provide a formulation of DPTs-II depending on the side of the ESQPT where the quench ends. We analyze the connections between various indicators of DPTs-II. Our results are numerically illustrated in the infinite-range transverse-field Ising model and are applicable to a large class of collective quantum systems satisfying a set of conditions.

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Signatures of excited-state quantum phase transitions in quantum many-body systems: Phase space analysis

Cited by 23 publications

References 120 publications

Theory of dynamical phase transitions in quantum systems with symmetry-breaking eigenstates

Theory of dynamical phase transitions in quantum systems with symmetry-breaking eigenstates

Energy cat states induced by a parity-breaking excited-state quantum phase transition

Dynamical and excited-state quantum phase transitions in collective systems

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