# Excited-state quantum phase transitions: Static and dynamic manifestations

**Advisor:** Pavel Cejnar (IPNP MFF CUNI)

**Funding:** Fully funded

**Website:** http://www-ucjf.troja.mff.cuni.cz/cejnar/

**Contact:** cejnar@ipnp.mff.cuni.cz

This Ph.D. topic is focused on a connection of two active areas of theoretical research in quantum many-body physics: (i) the investigation of general dynamical properties of complex quantum systems out of equilibrium, and (ii) the study of quantum phase transitions and their signatures in various quantum systems. Research in these fields is important not only because of its fundamental connotation (describing diversity of aspects of quantum dynamics), but also because of its potential applications in quantum information protocols. Recent rapid progress in the design of laboratory quantum simulators makes an increasing amount of theoretical predictions available to experimental tests and opens routes to their future applications.

The student will investigate various static and dynamic signatures of Excited-State Quantum Phase Transitions (ESQPTs) [1-6] in bound or unbound quantum systems depending on one or more control parameters [7-9]. The work will include theoretical analyses of ESQPTs in specific many-body systems with a finite number of collective degrees of freedom, with regard to possible experimental realization by means of suitable quantum simulators [9].

The static manifestations of ESQPTs will be studied in properties like the density of energy spectrum and expectation values of relevant observables in stationary states, and/or in the properties of equilibrium thermal states [10]. The dynamic manifestations of ESQPTs will be analyzed in the response to various kinds of external driving, with the aid of the geometric approach [11-13], and/or in more complex processes involving external driving and thermalization [14].

The research in these directions will be adapted to actual results and challenges that will appear during the solution. A part of the work can be performed in collaboration with the quantum experimental group at Palacky University in Olomouc.

Bibliography:

[1] M.A. Caprio, P. Cejnar, F. Iachello, Annals of Physics 323 (2008)
1106

[2] P. Stránský, M. Macek, P. Cejnar, Annals of Physics 345 (2014) 73

[3] P. Stránský, M. Macek, A. Leviatan, P. Cejnar, Annals of Physics 356
(2015) 57

[4] P. Stránský, P. Cejnar, Physics Letters A 380 (2016) 2637

[5] M. Macek, P. Stránský, A. Leviatan, P. Cejnar, Physical Review C 99 (2019)
064323

[6] P. Stránský, M. Šindelka, M. Kloc, P. Cejnar, Physical Review Letters 125
(2020) 020401

[7] T. Brandes, Phys. Rep. 408 (2005) 315

[8] Understanding Quantum Phase Transitions, edited by L.D. Carr (CRC press,
Boca Raton, 2011)

[9] C. Gardiner, P. Zoller: The Quantum World of Ultra-Cold Atoms and Light,
Books I, II and III (Imperial College Press, London, 2014, 2015, 2016)

[10] P. Cejnar, P. Stránský, Physics Letters A 381 (2017) 984

[11] M. Kloc, P. Stránský, P. Cejnar, Physical Review A 98 (2018) 013836

[12] A. Polkovnikov et al., Rev. Mod. Phys. 83 (2011) 863

[13] M. Kolodrubetz, D. Sels, P. Mehta, A. Polkovnikov, Physics Reports 697
(2017) 1

[14] M. Kloc, P. Cejnar, G. Schaller, Physical Review E 100 (2019) 042126