14 research outputs found
High order non-unitary split-step decomposition of unitary operators
We propose a high order numerical decomposition of exponentials of hermitean
operators in terms of a product of exponentials of simple terms, following an
idea which has been pioneered by M. Suzuki, however implementing it for complex
coefficients. We outline a convenient fourth order formula which can be written
compactly for arbitrary number of noncommuting terms in the Hamiltonian and
which is superiour to the optimal formula with real coefficients, both in
complexity and accuracy. We show asymptotic stability of our method for
sufficiently small time step and demonstrate its efficiency and accuracy in
different numerical models.Comment: 10 pages, 4 figures (5 eps files) Submitted to J. of Phys. A: Math.
Ge
Quantum phase transition in a far from equilibrium steady state of XY spin chain
Using quantization in the Fock space of operators we compute the
non-equilibrium steady state in an open Heisenberg XY spin 1/2 chain of finite
but large size coupled to Markovian baths at its ends. Numerical and
theoretical evidence is given for a far from equilibrium quantum phase
transition with spontaneous emergence of long-range order in spin-spin
correlation functions, characterized by a transition from saturation to linear
growth with the size of the entanglement entropy in operator space.Comment: 4 pages (in RevTex) with 5 figures - essentially identical with a
published versio
Time-dependent variational principle for quantum lattices
We develop a new algorithm based on the time-dependent variational principle applied to matrix product states to efficiently simulate the real-and imaginary-time dynamics for infinite one-dimensional quantum lattices. This procedure (i) is argued to be optimal, (ii) does not rely on the Trotter decomposition and thus has no Trotter error, (iii) preserves all symmetries and conservation laws, and (iv) has low computational complexity. The algorithm is illustrated by using both an imaginary-time and a real-time example
Loschmidt echoes in two-body random matrix ensembles
Fidelity decay is studied for quantum many-body systems with a dominant
independent particle Hamiltonian resulting e.g. from a mean field theory with a
weak two-body interaction. The diagonal terms of the interaction are included
in the unperturbed Hamiltonian, while the off-diagonal terms constitute the
perturbation that distorts the echo. We give the linear response solution for
this problem in a random matrix framework. While the ensemble average shows no
surprising behavior, we find that the typical ensemble member as represented by
the median displays a very slow fidelity decay known as ``freeze''. Numerical
calculations confirm this result and show, that the ground state even on
average displays the freeze. This may contribute to explanation of the
``unreasonable'' success of mean field theories.Comment: 9 pages, 5 figures (6 eps files), RevTex; v2: slight modifications
following referees' suggestion
Entanglement as a resource in adiabatic quantum optimization
We explore the role of entanglement in adiabatic quantum optimization by performing approximate simulations of the real-time evolution of a quantum system while limiting the amount of entanglement. To classically simulate the time evolution of the system with a limited amount of entanglement, we represent the quantum state using matrix-product states and projected entangledpair states. We show that the probability of finding the ground state of an Ising spin glass on either a planar or non-planar two-dimensional graph increases rapidly as the amount of entanglement in the state is increased. Furthermore, we propose evolution in complex time as a way to improve simulated adiabatic evolution and mimic the effects of thermal cooling of the quantum annealer