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Journal Article

Bipartite fidelity for models with periodic boundary conditions


Morin-Duchesne,  Alexi
Max Planck Institute for Mathematics, Max Planck Society;

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Morin-Duchesne, A., Parez, G., & Liénardy, J. (2021). Bipartite fidelity for models with periodic boundary conditions. Journal of Statistical Mechanics: Theory and Experiment, 2021(2): 023101. doi:10.1088/1742-5468/abc1eb.

Cite as: https://hdl.handle.net/21.11116/0000-0008-28FF-D
For a given statistical model, the bipartite fidelity $\mathcal F$ is
computed from the overlap between the groundstate of a system of size $N$ and
the tensor product of the groundstates of the same model defined on two
subsystems $A$ and $B$, of respective sizes $N_A$ and $N_B$ with $N = N_A +
N_B$. In this paper, we study $\mathcal F$ for critical lattice models in the
case where the full system has periodic boundary conditions. We consider two
possible choices of boundary conditions for the subsystems $A$ and $B$, namely
periodic and open. For these two cases, we derive the conformal field theory
prediction for the leading terms in the $1/N$ expansion of $\mathcal F$, in a
most general case that corresponds to the insertion of four and five fields,
respectively. We provide lattice calculations of $\mathcal F$, both exact and
numerical, for two free-fermionic lattice models: the XX spin chain and the
model of critical dense polymers. We study the asymptotic behaviour of the
lattice results for these two models and find an agreement with the predictions
of conformal field theory.