Holographic quantum states

TL;DR

This paper establishes a connection between continuous matrix product states in quantum field theories and dissipative boundary dynamics, enabling new analytical tools and interpretations for quantum phase transitions and measurement.

Contribution

It introduces a boundary field theory framework for continuous matrix product states, linking quantum measurement, field theory, and real-space renormalization without lattice discretization.

Findings

Correlation functions correspond to quantum jump statistics

Boundary theory enables renormalization group methods in higher dimensions

Provides a new interpretation of cavity QED experiments in quantum field theory

Abstract

We show how continuous matrix product states of quantum field theories can be described in terms of the dissipative non-equilibrium dynamics of a lower-dimensional auxiliary boundary field theory. We demonstrate that the spatial correlation functions of the bulk field can be brought into one-to-one correspondence with the temporal statistics of the quantum jumps of the boundary field. This equivalence: (1) illustrates an intimate connection between the theory of continuous quantum measurement and quantum field theory; (2) gives an explicit construction of the boundary field theory allowing the extension of real-space renormalization group methods to arbitrary dimensional quantum field theories without the introduction of a lattice parameter; and (3) yields a novel interpretation of recent cavity QED experiments in terms of quantum field theory, and hence paves the way toward observing genuine quantum phase transitions in such zero-dimensional driven quantum systems.