Excited-state quantum phase transitions

Abstract

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.

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

“…This ESQPT differs from the one in the LMG model; the ESQPTs in the CT model are identified by a nonanalyticity in the first derivative of the density of states at the critical energies. This can be explained due to the fact that the number of effective degrees of freedom in this model is f = 2 and, for a nondegenerate critical point, the nonanaliticity is expected to appear in the f − 1th derivative of the energy level density [43,75]. The difference between this case and the LMG case ( f = 1) is obvious comparing the LMG and CT density of states in Figs.…”

Work statistics and symmetry breaking in an excited-state quantum phase transition

“…We can identify ESQPTs either by fixing the energy while varying the control parameter of the model or, equivalently, by increasing the energy at a fixed value of the control parameter. The ESQPT refers to a nonanalytical behavior of the density 032145-2 of states ν(E ) = k δ(E − E k ) with E k the eigenenergies of the Hamiltonian, i.e., H = k E k |k k| [7,11]. As the system approaches an ESQPT in the LMG, the density of states develops a logarithmic divergence ν(E ) ∝ − log |E − E c | due to a concentration of the energy levels at E c = 0 [14,77,78] and for h < 1 which is the critical region for the ESQPT in the Hamiltonian (4).…”

“…While typically QPTs are exhibited in the ground state of a many-body system, certain special Hamiltonians may give rise to so-called excited-state quantum phase transitions (ESQPTs) [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Like their more traditional counterpart, ESQPTs are characterized by a similarly closing energy gap between excited states and, additionally, the density of states becomes singular around a critical excitation energy.…”

“…Symmetric ground state. (a), (b) The survival probability(7) and the work probability distribution(9), respectively, for a system size N = 2000 and initial magnetic field h i = 0.5, when the quench is performed to below (h f = 0.6), above (h f = 0.9), and at the ESQPT critical point (h f = 0.75). (c) The Shannon entropy(11) with respect to the magnetic field h f for various system sizes N = 100[bottom, blue] → 1000[top, cyan], the inset show the scaling of the maximum of S W with respect to log 2 (N ).…”

Dynamical preparation of stripe states in spin-orbit-coupled gases

“…Such a Hamiltonian explains several quantum many-body phenomena in spinor condensates [34,35], including the generation of macroscopic entanglement [36][37][38][39][40][41][42][43][44][45][46][47][48][49], with potential metrological applications [50], and the observation of nonequilibrium phenomena such as the formation of spin domains and topological defects [51][52][53][54][55][56][57][58][59][60][61]. Recently, dynamical [62] and excitedstate [63] quantum phase transitions have been theoretically [64,65] and experimentally [66,67] studied in spin-1 BECs with spin-changing collisions. Here we exploit this map to provide a many-body protocol to access the ferromagnetic stripe phase of the SOC gas via crossing a quantum phase transition of the low-energy Hamiltonian in an excited state.…”