Estimating entanglement monotones of non-pure permutationally invariant spin states

Estimating entanglement monotones of non-pure permutationally invariant spin states

Seminar author:Julia Mathe

Event date and time:06/13/2025 02:30:pm

Event location:Seminars Room, GIQ

Event contact:

One way to characterize complex many-body systems is to investigate their entanglement structure. Given a mixed many-body state, we ask:How can we find lower bounds and upper bounds to a given entanglement monotone?How tight are these bounds and can we actually compute them for large systems?To answer these questions, we present methods to find such lower and upper bounds based on entanglement witnesses and separable ansatz states, respectively, and elaborate on how symmetries can help us to significantly simplify these methods. Focusing on spin systems on fully-connected graphs nonzero temperature, we derive lower bounds to distances from the set of fully separable states based on spin-squeezing inequalities. These are combinations of variances of collective spin operators and are potentially close to optimal in the large particle-number limit, at least for models with two-particle interactions.  Concretely, we apply our methods to equilibrium states of the permutation-invariant XXZ model with an external field and investigate entanglement close to quantum phase transitions (QPTs). We observe that our lower bound becomes tight for zero temperature as well as for the temperature at which entanglement disappears, both of which are thus precisely captured by the spin-squeezing inequalities. We further observe, among other things, that entanglement arises at nonzero temperature close to a QPT even in the ordered phase, where the ground state is separable. This can be considered an entanglement signature of a QPT that may also be visible in experiments.

Reference: https://arxiv.org/abs/2504.07814