scholarly journals Finite-size corrections in critical symmetry-resolved entanglement

2021 ◽  
Vol 10 (3) ◽  
Author(s):  
Benoit Estienne ◽  
Yacine Ikhlef ◽  
Alexi Morin-Duchesne
Keyword(s):  
Symmetry Group ◽  
Crucial Role ◽  
Entanglement Entropy ◽  
Scaling Limit ◽  
Finite Size ◽  
Discrete Symmetry ◽  
System Size ◽  
Quantum Systems ◽  
Finite Size Corrections

In the presence of a conserved quantity, symmetry-resolved entanglement entropies are a refinement of the usual notion of entanglement entropy of a subsystem. For critical 1d quantum systems, it was recently shown in various contexts that these quantities generally obey entropy equipartition in the scaling limit, i.e. they become independent of the symmetry sector. In this paper, we examine the finite-size corrections to the entropy equipartition phenomenon, and show that the nature of the symmetry group plays a crucial role. In the case of a discrete symmetry group, the corrections decay algebraically with system size, with exponents related to the operators' scaling dimensions. In contrast, in the case of a U(1) symmetry group, the corrections only decay logarithmically with system size, with model-dependent prefactors. We show that the determination of these prefactors boils down to the computation of twisted overlaps.

Finite-Size Corrections in the Supersymmetric t–J Model with Boundary Fields

1997 ◽  
Vol 11 (09) ◽  
pp. 1137-1151 ◽  
Author(s):  
Hitoshi Asakawa ◽  
Masuo Suzuki
Keyword(s):  
Ground State ◽  
State Energy ◽  
Present Model ◽  
Scaling Limit ◽  
Finite Size ◽  
Partition Functions ◽  
Excitation Energies ◽  
Ground State Degeneracy ◽  
Boundary Fields ◽  
Finite Size Corrections

The supersymmetric t–J model with boundary fields is discussed. Using the exact solution of the present model, the finite-size corrections of the ground-state energy and the low-lying excitation energies are calculated. The partition functions are evaluated in the scaling limit to obtain the conformal weights of the primary fields in the present model. A surface critical exponent and the ground-state degeneracy are also derived.

scholarly journals SIMPLICIAL QUANTUM GRAVITY ON A RANDOMLY TRIANGULATED SPHERE

1999 ◽  
Vol 14 (24) ◽  
pp. 3885-3903 ◽  
Author(s):  
CHRISTIAN HOLM ◽  
WOLFHARD JANKE
Keyword(s):  
Quantum Gravity ◽  
Scaling Limit ◽  
Finite Size ◽  
System Size ◽  
Finite Size Scaling ◽  
Corrections To Scaling ◽  
Regge Calculus ◽  
Expectation Value ◽  
Size Scaling ◽  
Scaling Analyses

We study 2D quantum gravity on spherical topologies employing the Regge calculus approach with the dl/l measure. Instead of the normally used fixed nonregular triangulations we study random triangulations which are generated by the standard Voronoi–Delaunay procedure. For each system size we average the results over four different realizations of the random lattices. We compare both types of triangulations quantitatively and investigate how the difference in the expectation value of the squared curvature, R2, for fixed and random triangulations depends on the lattice size and the surface area A. We try to measure the string susceptibility exponents through finite-size scaling analyses of the expectation value of an added R2 interaction term, using two conceptually quite different procedures. The approach, where an ultraviolet cutoff is held fixed in the scaling limit, is found to be plagued with inconsistencies, as has already previously been pointed out by us. In a conceptually different approach, where the area A is held fixed, these problems are not present. We find the string susceptibility exponent γ′ str in rough agreement with theoretical predictions for the sphere, whereas the estimate for γ str appears to be too negative. However, our results are hampered by the presence of severe finite-size corrections to scaling, which lead to systematic uncertainties well above our statistical errors. We feel that the present methods of estimating the string susceptibilities by finite-size scaling studies are not accurate enough to serve as testing grounds to decide the success or failure of quantum Regge calculus.

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