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Signal propagation in lattice models of quantum many-body systems

Charles Radin

Communications in Mathematical PhysicsJun 1, 19784 citations

Information propagation for interacting-particle systems

Norbert Schuch, Sarah K. Harrison, Tobias J. Osborne +1 more

We study the speed at which information propagates through systems of interacting quantum particles moving on a regular lattice and show that for a certain class of initial conditions there exists a maximum speed of sound at which information can propagate. Our argument applies equally to quantum spins, bosons such as in the Bose-Hubbard model, fermions, anyons, and general mixtures thereof, on arbitrary lattices of any dimension. It also pertains to dissipative dynamics on the lattice, and generalizes to the continuum for quantum fields. Our result can be seen as an analog of the Lieb-Robinson bound for strongly correlated models.We study the speed at which information propagates through systems of interacting quantum particles moving on a regular lattice and show that for a certain class of initial conditions there exists a maximum speed of sound at which information can propagate. Our argument applies equally to quantum spins, bosons such as in the Bose-Hubbard model, fermions, anyons, and general mixtures thereof, on arbitrary lattices of any dimension. It also pertains to dissipative dynamics on the lattice, and generalizes to the continuum for quantum fields. Our result can be seen as an analog of the Lieb-Robinson bound for strongly correlated models.

arXiv:1010.4576Physical Review ASep 8, 201162 citations

Non-local propagation of correlations in long-range interacting quantum systems

A.C. Lee, Philip Richerme, Zhihao Gong +6 more

Bulletin of the American Physical SocietyJun 4, 20149 citations

Non-local propagation of correlations in quantum systems with long-range interactions

Philip Richerme, Zhexuan Gong, Aaron Lee +6 more

arXiv:1401.5088NatureJul 8, 2014790 citations

Quantum and Classical Correlations in Waveguide Lattices

Yaron Bromberg, Yoav Lahini, Roberto Morandotti +1 more

We study quantum and classical Hanbury Brown-Twiss correlations in waveguide lattices. We develop a theory for the propagation of photon pairs in the lattice, predicting the emergence of nontrivial quantum interferences unique to lattice systems. Experimentally, we observe the classical counterpart of these interferences using intensity-correlation measurements. We discuss the correspondence between the classical and quantum correlations, and consider path-entangled input states which do not have a classical analogue. Our results demonstrate that waveguide lattices can be used as a robust and highly controllable tool for manipulating quantum states, and offer new ways of studying the quantum properties of light.We study quantum and classical Hanbury Brown-Twiss correlations in waveguide lattices. We develop a theory for the propagation of photon pairs in the lattice, predicting the emergence of nontrivial quantum interferences unique to lattice systems. Experimentally, we observe the classical counterpart of these interferences using intensity-correlation measurements. We discuss the correspondence between the classical and quantum correlations, and consider path-entangled input states which do not have a classical analogue. Our results demonstrate that waveguide lattices can be used as a robust and highly controllable tool for manipulating quantum states, and offer new ways of studying the quantum properties of light.

arXiv:0807.3938Physical Review LettersJun 26, 2009318 citations

Spread of correlations in strongly disordered lattice systems with long-range coupling

Karol Kawa, Paweł Machnikowski

We investigate the spread of correlations in a one-dimensional lattice system with high on-site energy disorder and long-range couplings with a power-law dependence on the distance ($\ensuremath{\propto}{r}^{\ensuremath{-}\ensuremath{\mu}}$). The increase in correlation between the initially quenched node and a given node exhibits three phases: quadratic in time, linear in time, and saturation. No further evolution is observed in the long time regime. We find an approximate solution of the model valid in the limit of strong disorder and reproduce the results of numerical simulations with analytical formulas. We also find the time needed to reach a given correlation value as a measure of the propagation speed. Because of the triple-phase evolution of the correlation function, the propagation changes its time dependence. In the particular case of $\ensuremath{\mu}=1$, the propagation starts as a ballistic motion and then, at a certain crossover time, turns into standard diffusion.We investigate the spread of correlations in a one-dimensional lattice system with high on-site energy disorder and long-range couplings with a power-law dependence on the distance ($\ensuremath{\propto}{r}^{\ensuremath{-}\ensuremath{\mu}}$). The increase in correlation between the initially quenched node and a given node exhibits three phases: quadratic in time, linear in time, and saturation. No further evolution is observed in the long time regime. We find an approximate solution of the model valid in the limit of strong disorder and reproduce the results of numerical simulations with analytical formulas. We also find the time needed to reach a given correlation value as a measure of the propagation speed. Because of the triple-phase evolution of the correlation function, the propagation changes its time dependence. In the particular case of $\ensuremath{\mu}=1$, the propagation starts as a ballistic motion and then, at a certain crossover time, turns into standard diffusion.

arXiv:2106.08240Physical review. B./Physical review. BMay 18, 20221 citation

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