TY  - JOUR
A1  - Riera, Arnau
A1  - Gogolin, Christian
A1  - Eisert, Jens
T1  - Thermalization in nature and on a quantum computer
JF  - Physical review letters
N2  - In this work, we show how Gibbs or thermal states appear dynamically in closed quantum many-body systems, building on the program of dynamical typicality. We introduce a novel perturbation theorem for physically relevant weak system-bath couplings that is applicable even in the thermodynamic limit. We identify conditions under which thermalization happens and discuss the underlying physics. Based on these results, we also present a fully general quantum algorithm for preparing Gibbs states on a quantum computer with a certified runtime and error bound. This complements quantum Metropolis algorithms, which are expected to be efficient but have no known runtime estimates and only work for local Hamiltonians.
Y1  - 2012
U6  - https://doi.org/10.1103/PhysRevLett.108.080402
SN  - 0031-9007
VL  - 108
IS  - 8
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - JOUR
A1  - Caravelli, Francesco
A1  - Hamma, Alioscia
A1  - Markopoulou, Fotini
A1  - Riera, Arnau
T1  - Trapped surfaces and emergent curved space in the Bose-Hubbard model
JF  - Physical review : D, Particles, fields, gravitation, and cosmology
N2  - A Bose-Hubbard model on a dynamical lattice was introduced in previous work as a spin system analogue of emergent geometry and gravity. Graphs with regions of high connectivity in the lattice were identified as candidate analogues of spacetime geometries that contain trapped surfaces. We carry out a detailed study of these systems and show explicitly that the highly connected subgraphs trap matter. We do this by solving the model in the limit of no back-reaction of the matter on the lattice, and for states with certain symmetries that are natural for our problem. We find that in this case the problem reduces to a one-dimensional Hubbard model on a lattice with variable vertex degree and multiple edges between the same two vertices. In addition, we obtain a (discrete) differential equation for the evolution of the probability density of particles which is closed in the classical regime. This is a wave equation in which the vertex degree is related to the local speed of propagation of probability. This allows an interpretation of the probability density of particles similar to that in analogue gravity systems: matter inside this analogue system sees a curved spacetime. We verify our analytic results by numerical simulations. Finally, we analyze the dependence of localization on a gradual, rather than abrupt, falloff of the vertex degree on the boundary of the highly connected region and find that matter is localized in and around that region.
Y1  - 2012
U6  - https://doi.org/10.1103/PhysRevD.85.044046
SN  - 1550-7998
VL  - 85
IS  - 4
PB  - American Physical Society
CY  - College Park
ER  -