One of the central research problems in theoretical physics is the dynamics of quantum many-body systems. A challenging open problem is the numerical simulation of out-of-equilibrium dynamics in continuous strongly-interacting models of quantum field theory, which in contrast to lattice models remain hard to study. This has recently become a pressing task, due to rapid advances in ultra-cold atom experiments that have achieved a realisation of the sine-Gordon model, a one-dimensional quantum field theory exhibiting topological excitations.
The proposed research aims at:
1. The development of a new numerical technique to be named “Tensor Network Truncated Conformal Space Approach” (TNTCSA) for the numerical simulation of quantum dynamics in continuous one-dimensional and strongly-interacting models of significant experimental interest. The method will be built upon the standard TCSA method optimised by using an efficient adaptive truncation scheme, based on Tensor Network techniques also used in the Density Matrix Renormalisation Group and Matrix Product State methods.
2. The application of the new method for the simulation of the above mentioned ultra-cold atom experiments, both in and out of equilibrium. We will compute theoretical predictions for equilibrium and dynamical correlations of the quantum sine-Gordon model and compare with experimental data to obtain a precise modelling of the experimental system.
3. Building upon this, we will devise a blueprint for experimentally realising a quantum field thermal machine, whose operation will be based on the application of controllable space and time dependent external potentials.
The new method is expected to have applications in a broad range of physics areas from particle physics to statistical mechanics and atomic physics.
Fields of science
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