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arXiv:0707.0325 · Annals of Physics

Excited state quantum phase transitions in many-body systems

M.A. Caprio, Pavel Cejnar, FRANCESCO IACHELLO

Published Jul 11, 2007• 281 citations
arXivHTMLPDF
DOI
10.1016/j.aop.2007.06.011

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By analyzing the probability distributions of the Loschmidt echo (LE) and quantum work, we examine the nonequilibrium effects of a quantum many-body system, which exhibits an excited-state quantum phase transition (ESQPT). We find that depending on the value of the controlling parameter the distribution of the LE displays different patterns. At the critical point of the ESQPT, both the averaged LE and the averaged work show a cusplike shape. Furthermore, by employing the finite-size scaling analysis of the averaged work, we obtain the critical exponent of the ESQPT. Finally, we show that at the critical point of ESQPT the eigenstate is a highly localized state, further highlighting the influence of the ESQPT on the properties of the many-body system.
Identifying dynamical signatures of excited-state quantum phase transitions (ESQPTs) in experimentally realizable quantum many-body systems is helpful for understanding the dynamical effects of ESQPTs. In such systems, the highly controllable spinor Bose-Einstein condensates (BECs) offer an exceptional platform to study ESQPTs. In this work, we investigate the dynamical characteristics of the ESQPT in spin-1 BEC by means of the Loschmidt echo spectrum. The Loschmidt echo spectrum is an extension of the well-known Loschmidt echo and defined as the overlaps between the evolved state and the excited states of the initial Hamiltonian. We show that both the time-evolved and long-time-averaged Loschmidt echo spectrum undergo a remarkable change as the system passes through the critical point of the ESQPT. Moreover, the particular behavior exhibited by the Loschmidt echo spectrum at the critical point stands as a dynamical detector for probing the ESQPT. We further demonstrate how to capture the features of the ESQPT by using the energy distribution associated with the Loschmidt echo spectrum for time-evolved and long-time-averaged cases, respectively. Our findings contribute to a further verification of the usefulness of the Loschmidt echo spectrum for witnessing various quantum phase transitions in many-body systems and provide a different way to experimentally examine the dynamical consequences of ESQPTs.