Classical and quantum matrix product states: exploring the structure of non-equilibrium states

A quiet revolution has occurred in the last decade in the understanding of low-dimensional correlated quantum systems. The use of theories based on matrix product states has provided a reliable, controlled approximation scheme that can accurately describe the low energy states, as well as the dynamics of many models. The approach is based on representing the state by a product of matrices, where the internal dimension of the matrix encodes correlations in the state. It has been shown that this underlying structure, a matrix product state (MPS), is the source of the reliability and efficiency of the density matrix renormalisation group (DMRG) approximation used for computation of quantum states. Crucially, such an approximation also allows efficient simulation of quantum dynamics, via time-evolving block decimation (TEBD). Recently, the same technique has begun to be applied to open quantum systems.
Remarkably, while such techniques have come to the fore relatively recently in the context of quantum systems, they have a far longer history for classical systems. In particular, in the archetypal TASEP problem (totally asymmetric exclusion process which is a fundamental classical system driven out of equilibrium), a closed form analytic solution can be found in terms of exactly the same matrix product state structure. Moreover, recent progress has been made in understanding the link between the existence of matrix product or more complicated tensor product states for one- dimensional classical driven systems and integrability via the algebraic Bette ansatz.
Although there important distinctions - for classical problems, the matrix product state is a representation of the probability distribution, whereas for quantum systems it represents the state, and for open quantum systems, it represents the density matrix - there is potential for significant crossover between the quantum and classical cases. As yet, however, there has been very little exchange between the classical and quantum communities using these techniques. The aim of this workshop is to rectify this.

Registration is now open, the cost is £60 which includes lunch and refreshments on both days and a conference dinner on 10th September. To register, please following the link below and complete your registration by 26th August.

Registration Link

PRACTICAL ARRANGEMENTS

Workshop venue - The workshop will take place in the meeting room of the Higgs Centre for Theoretical Physics, which is located on the 4th Floor of the James Clerk Maxwell Building on the King's Buildings campus of the University of Edinburgh. The full programme is attached to this webpage, there will be signs for the workshop directing you from the main entrance.

Getting to the James Clerk Maxwell Building - Click here for directions to the JCMB by various modes of transport. The directions provided by Google Maps are much improved these days, and will give you accurate instructions to the main entrance of JCMB - click here for a map with a pin in the right place. Click "Directions" (top left), enter your starting point, choose your mode of transport (car, bus, foot), and you're done.

Please note that it is very important that you enter via the main entrance, otherwise getting horribly lost is an almost certainty. Briefly, if you arrive on the 41 bus (destination "King's Buildings" - do not board any other 41 bus) you should alight at the final bus stop which is on campus. Head south towards the Scottish Agricultural College (this is the direction the bus will have been travelling just before arrival). Turn left, and JCMB is in front of you behind a circular architectural feature that is impossible to describe in words, but will be immediately recognisable. If you walk to the campus, or arrive on any other bus, aim for Gate 4 onto the King's Buildings Campus, which is on Mayfield Road opposite Blackbarony Road (see map). Follow the road onto the campus until it forks. Take the right fork (signposted "Magnet Cafe"): the steps that lie far ahead of you take you right into the main entrance of JCMB.