A sudden quantum quench of a Bloch band from one topological phase toward another has been shown to exhibit an intimate connection with the notion of a dynamical quantum phase transition (DQPT), where the returning probability of the quenched state to the initial state—i.e. the Loschmidt echo—vanishes at critical times $\{t^*\}$. Analytical results to date are limited to two-band models, leaving the exact relation between topology and DQPT unclear. In this work, we show that for a general multi-band system, a robust DQPT relies on the existence of nodes (i.e. zeros) in the wavefunction overlap between the initial band and the post-quench energy eigenstates. These nodes are topologically protected if the two participating wavefunctions have distinctive topological indices. We demonstrate these ideas in detail for both one and two spatial dimensions using a three-band generalized Hofstadter model. We also discuss possible experimental observations.
*US DOE BES E304/E3B7, ERC DM 321031
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Authors
Zhoushen Huang
Los Alamos National Laboratory
Alexander Balatsky
Nordita, KTH Royal Institute of Technology, Stockholm University and Los Alamos National Laboratory
Nordita, KTH Royal Institute of Technology and Stockholm University; Institute for Materials Science, Los Alamos National Laboratory, USA
Nordita, Center for Quantum Materials, KTH Royal Institute of Technology and Stockholm University, Stockholm, Sweden
Nordita, KTH Royal Institute of Technology and Stockholm University; Institute for Materials Science, Los Alamos National Laboratory
Los Alamos National Laboratory, NORDITA
Institute for Materials Science, Los Alamos National Laboratory, USA; Nordita, KTH Royal Institute of Technology and Stockholm University, Sweden
Nordita, Center for Quantum Materials, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden
Nordita, Center for Quantum Materials, Stockholm University and KTH, Stockholm and Institute for Materials Science, LANL, Los Alamos, USA
