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arXiv · 1701.03911

Emergent topology and dynamical quantum phase transitions in two-dimensional closed quantum systems

Utso Bhattacharya·Amit Dutta
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Abstract

We introduce the notion of a dynamical topological order parameter (DTOP) that characterises dynamical quantum phase transitions (DQPTs) occurring in the subsequent temporal evolution of "two dimensional" closed quantum systems, following a quench (or ramping) of a parameter of the Hamiltonian, {which generalizes the notion of DTOP introduced in Budich and Heyl, Phys. Rev. B 93, 085416 (2016) for one-dimensional situations}. This DTOP is obtained from the "gauge-invariant" Pancharatnam phase extracted from the Loschmidt overlap, i.e., the modulus of the overlap between the initially prepared state and its time evolved counterpart reached following a temporal evolution generated by the time-independent final Hamiltonian. This generic proposal is illustrated considering DQPTs occurring in the subsequent temporal evolution following a sudden quench of the staggered mass of the topological Haldane model on a hexagonal lattice where it stays fixed to zero or unity and makes a discontinuous jump between these two values at critical times at which DQPTs occur.

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Utso Bhattacharya, Amit Dutta. 2017-01-21. Emergent topology and dynamical quantum phase transitions in two-dimensional closed quantum systems. https://doi.org/10.1103/physrevb.96.014302

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