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Czarnik P.,Center for Complex Systems Research | Dziarmaga J.,Center for Complex Systems Research
Physical Review B - Condensed Matter and Materials Physics | Year: 2014

An algorithm for imaginary time evolution of a fermionic projected entangled pair state with ancillas from infinite temperature down to a finite temperature state is presented. As a benchmark application, it is applied to spinless fermions hopping on a square lattice subject to p-wave pairing interactions. With a tiny bias it allows one to evolve the system across a high-temperature continuous symmetry-breaking phase transition. © 2014 American Physical Society.


Dziarmaga J.,Center for Complex Systems Research | Tylutki M.,Center for Complex Systems Research | Zurek W.H.,Los Alamos National Laboratory | Zurek W.H.,University of Ulm
Physical Review B - Condensed Matter and Materials Physics | Year: 2012

We study a linear ramp of the nearest-neighbor tunneling rate in the Bose-Hubbard model driving the system from the Mott insulator state into the superfluid phase. We employ the truncated Wigner approximation to simulate linear quenches of a uniform system in one, two, and three dimensions, and in a harmonic trap, in three dimensions. In all these setups, the excitation energy decays like one over third root of the quench time. The -1/3 scaling arises from an impulse-adiabatic approximation-a variant of the Kibble-Zurek mechanism-describing a crossover from nonadiabatic to adiabatic evolution when the system begins to keep pace with the increasing tunneling rate. © 2012 American Physical Society.


Czarnik P.,Center for Complex Systems Research | Cincio L.,Perimeter Institute for Theoretical Physics | Dziarmaga J.,Center for Complex Systems Research
Physical Review B - Condensed Matter and Materials Physics | Year: 2012

A projected entangled pair state (PEPS) with ancillas is evolved in imaginary time. This tensor network represents a thermal state of a two-dimensional (2D) lattice quantum system. A finite-temperature phase diagram of the 2D quantum Ising model in a transverse field is obtained as a benchmark application. © 2012 American Physical Society.

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