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Quantum field theory, the variational principle, and continuous matrix product states

Objective

Quantum field theories, quantum systems with an infinite number of degrees of freedom, present the most subtle and complex systems in physics. At the same time, the study of quantum field theory has provided us with some of the most powerful theoretical tools to study many particle quantum systems. Many of the major insights in this theory have been obtained using the powerful technology of perturbation theory, whereas a main source of nonperturbative results has been lattice gauge theory. The variational principle has not met with as much systematic success in explaining these systems due to the dearth of good variational wavefunctions.

In condensed matter physics we have recently witnessed tremendous progress, spurred by developments in quantum information theory, in understanding the properties of physical states of strongly interacting many particle quantum systems. This has culminated in the realisation that the physics of low-dimensional systems is well captured by variational classes known as matrix product states, projected entangled-pair states, and the multiscale entanglement renormalisation ansatz. Very recently a continuum generalisation of the matrix product state variational class has been developed which promises to afford, via the variational principle, new insights into the behaviour of strongly interacting quantum field theory.

The purpose of this proposal is to: (a) understand how to use the variational principle to simulate the dynamics, both imaginary and real-time, of (1+1)- and higher-dimensional quantum field theories within the continuum matrix product state variational class; (b) extend the recent theoretical advances in the field of locally interacting quantum spin systems to study the correlation structure of equilibrium and non-equilibrium quantum fields; and (c) relate the developed formalism to cavity QED and hence develop experimental proposals to simulate strongly interacting quantum field theories with cavity QED systems.

Field of science

  • /natural sciences/physical sciences/condensed matter physics
  • /natural sciences/physical sciences/quantum physics/quantum field theory

Call for proposal

ERC-2011-StG_20101014
See other projects for this call

Funding Scheme

ERC-SG - ERC Starting Grant

Host institution

GOTTFRIED WILHELM LEIBNIZ UNIVERSITAET HANNOVER
Address
Welfengarten 1
30167 Hannover
Germany
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 1 343 219,10
Principal investigator
Tobias Osborne (Prof.)
Administrative Contact
Elke Buchholz (Ms.)

Beneficiaries (1)

GOTTFRIED WILHELM LEIBNIZ UNIVERSITAET HANNOVER
Germany
EU contribution
€ 1 343 219,10
Address
Welfengarten 1
30167 Hannover
Activity type
Higher or Secondary Education Establishments
Principal investigator
Tobias Osborne (Prof.)
Administrative Contact
Elke Buchholz (Ms.)