ELFT HÍRADÓ

[Kormos Márton <kormos.marton AT ttk.bme.hu>]

MEGHÍVÓ

BME Elméleti Fizika Szeminárium,

márc. 13. péntek 10h15,

1111 Budapest, Budafoki út 8., BME F III. magasföldszint 01.,
Elméleti Fizika Tanszék szemináriumi szoba

Riccarda Bonsignori (BME Elm. Fiz. Tanszék)
Entanglement Hamiltonian after a local quench

Understanding the structure of entanglement in extended quantum systems is a 
fundamental problem in theoretical physics. In this framework, a central 
object is the so-called entanglement (or modular) Hamiltonian (EH), defined 
as the logarithm of the reduced density matrix, that encodes the full 
structure of bipartite entanglement. In general the EH  is very hard to 
compute and is not even expected to be a local operator.  However, in 
relativistic quantum field theory the locality of the modular Hamiltonian for 
half-space bipartitions is ensured by the Bisognano–Wichmann theorem, which 
expresses it as an integral of the energy density with a linear spatial 
weight. In the presence of conformal symmetry, this result can be extended to 
other geometries and to some non-equilibrium settings. Since the 
Bisognano–Wichmann theorem is formulated within relativistic quantum field 
theory, a natural question concerns its applicability to lattice many-body 
systems whose low-energy properties are described by a conformal field 
theory, but which explicitly break Lorentz invariance. Several results 
addressing this question exist in equilibrium situations, while a lattice 
realisation of the time-dependent EH in out-of-equilibrium dynamics is still 
missing.

In this talk, I will present the study of the dynamics of the EH in a system 
of one-dimensional free fermions, following a local joining quench of two 
initially disconnected half-chains in their ground states. Applying 
techniques of conformal field theory, a local expression of the EH is 
derived, where the left- and right-moving components of the energy density 
are associated with different weight functions.

The results are then compared to numerical calculations for the hopping 
chain, which requires to consider a proper continuum limit of the lattice EH, 
obtaining a good agreement with the field-theory prediction.


Minden érdeklődőt szeretettel várunk.

A további program megtekinthető itt: https://dtp.physics.bme.hu/TheorySeminars

Kormos Márton,
szeminárium koordinátor