The Entanglement perspectives on the quantum many body problem
Lead Research Organisation:
University of Strathclyde
Department Name: Physics
Abstract
Background and state of the Art
Quantum many body systems are systems made by several constituent, such as for example materials, made by atoms, or light made by photons or nuclei made by nucleons.
Complexity of quantum many body systems Quantum many body systems are described by complex wave functions whose number of parameters increases exponentially with the number of constituents thus effectively limiting our capability to study them.
Tensor networks In specific cases, like for example when studying the equilibrium state of many body systems described with local enough Hamiltonians, tensor networks provide a polynomial description of the exponentially large state of many body quantum systems. Tensor networks are constructed from small elementary tensors contracted in a specific pattern dictated by the geometry of the network.
Geometry of tensor networks the geometry of the network completely determines the patterns of correlations in the state it describes. For this reason there is a connection between the structure of entanglement at equilibrium and the geometry of the tensor network and tensor networks are best suited to describe local correlations.
Out of equilibrium, During the out-of-equilibrium evolution short range correlations radiate into long range correlations and thus traditional tensor networks chase to provide good description of the many body wave function.
Research hypothesis and objectives
Our objective is to find a possible descriptions of the out-of-equilibrium dynamics of a many body quantum systems in term of tensor networks.
We will
1) apply the intuition that despite the fact that during the out-of-equilibrium evolution long range entanglement is created, the correlations are still short ranged. In this way we will devise a strategy to perform approximate out of equilibrium of many body quantum states that will allow to get the correct evolutions of local observables.
2) characterize and understand advanced tensor network structures such as the spectral tensor networks and the branching MERAs and adapt them to perform the out of equilibrium evolution of quantum systems.
Quantum many body systems are systems made by several constituent, such as for example materials, made by atoms, or light made by photons or nuclei made by nucleons.
Complexity of quantum many body systems Quantum many body systems are described by complex wave functions whose number of parameters increases exponentially with the number of constituents thus effectively limiting our capability to study them.
Tensor networks In specific cases, like for example when studying the equilibrium state of many body systems described with local enough Hamiltonians, tensor networks provide a polynomial description of the exponentially large state of many body quantum systems. Tensor networks are constructed from small elementary tensors contracted in a specific pattern dictated by the geometry of the network.
Geometry of tensor networks the geometry of the network completely determines the patterns of correlations in the state it describes. For this reason there is a connection between the structure of entanglement at equilibrium and the geometry of the tensor network and tensor networks are best suited to describe local correlations.
Out of equilibrium, During the out-of-equilibrium evolution short range correlations radiate into long range correlations and thus traditional tensor networks chase to provide good description of the many body wave function.
Research hypothesis and objectives
Our objective is to find a possible descriptions of the out-of-equilibrium dynamics of a many body quantum systems in term of tensor networks.
We will
1) apply the intuition that despite the fact that during the out-of-equilibrium evolution long range entanglement is created, the correlations are still short ranged. In this way we will devise a strategy to perform approximate out of equilibrium of many body quantum states that will allow to get the correct evolutions of local observables.
2) characterize and understand advanced tensor network structures such as the spectral tensor networks and the branching MERAs and adapt them to perform the out of equilibrium evolution of quantum systems.
Organisations
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/N509760/1 | 01/10/2016 | 30/09/2021 | |||
| 1812047 | Studentship | EP/N509760/1 | 01/10/2016 | 31/03/2020 | Jacopo Surace |
| Description | In the context of many body quantum physics one of the biggest challanges is being able to efficiently simulate the long time out-of-equilibrium dynamics of many body systems . We observed how, for a restricted class of systems (i.e. a class of closed quantum system that are expected to locally thermalise), this evolution can be locally efficiently approximated focussing on the exact local description of the system at each time step of the simulation. Under specific circumstances, an algorithm able to preserve at each step of the evolution the local properties of the system would be able to predict with good precision the approximated equilibrium state. We have presented a specific algorithm incorporating this ideas. The algorithm returns a good approximation of the desired state in the context of free systems. A closed path: We started developing techniques able to trade part of the entanglement of a pure state for mixedness and it seems, but at the moment it is not totally sure, that such kind of techniques will always introduce some approximation. Specifically, we studied these kind of techniques in the context of Gaussian Fermionic systems. Here, in order to trade entanglement for mixedness, the idea is to promote the eigenvalues of entangled modes of reduced density matrices to global eigenvalues. We did't find any viable method to do so without introducing approximations on global the energy of the state. In a second project, that we have submitted for publication, we discovered some universal properties for some quantum systems out of equilibrium. |
| Exploitation Route | A possible path would be implementing a similar algorithm in the context of interacting systems with tensor network techniques. We already presented the general strategy to follow in order to do so, but an actual algorithm is not been written yet. Our finding may be put on use in the simulation of many body thermalising systems. |
| Sectors | Chemicals,Digital/Communication/Information Technologies (including Software),Electronics,Energy,Pharmaceuticals and Medical Biotechnology |
| URL | https://arxiv.org/abs/1909.07381 |