We study the role of finite-size effects on critical behavior near a metallic $q=0$ critical point and compare the results with a recent extensive quantum Monte Carlo (QMC) study [Y. Schattner et al., Phys. Rev. X 6, 031028 (2016)]. This study found several features in both bosonic and fermionic responses, in disagreement with the expected critical behavior with a dynamical exponent $z=3$ . We show that finite-size effects are particularly strong for $z=3$ criticality and give rise to a behavior different from that of an infinite system, over a wide range of momenta and frequencies. We argue that by taking finite-size effects into account, the QMC results can be explained within $z=3$ theory.We study the role of finite-size effects on critical behavior near a metallic $q=0$ critical point and compare the results with a recent extensive quantum Monte Carlo (QMC) study [Y. Schattner et al., Phys. Rev. X 6, 031028 (2016)]. This study found several features in both bosonic and fermionic responses, in disagreement with the expected critical behavior with a dynamical exponent $z=3$. We show that finite-size effects are particularly strong for $z=3$ criticality and give rise to a behavior different from that of an infinite system, over a wide range of momenta and frequencies. We argue that by taking finite-size effects into account, the QMC results can be explained within $z=3$ theory.

arXiv:1701.07557Physical review. B./Physical review. BJul 27, 20173 citations

Finite Size Effects in Critical Phenomena.

Jia Liang Han

Jan 1, 19870 citations

Finite size scaling for the many-body-localization transition: finite-size-pseudo-critical points of individual eigenstates

Cécile Monthus

Abstract To understand the finite-size-scaling properties of phases transitions in classical and quantum models in the presence of quenched disorder, it has proven to be fruitful to introduce the notion of a finite-size-pseudo-critical point in each disordered sample and to analyze its sample-to-sample fluctuations as a function of the size. For the many-body-localization transition, where very strong eigenstate-to-eigenstate fluctuations have been numerically reported even within a given disordered sample at a given energy density (Yu, Luitz and Clark 2016 arXiv: 1606.01260 and Khemani, Lim, Sheng and Huse 2016 arXiv: 1607.05756 ), it seems thus useful to introduce the notion of a finite-size-pseudo-critical point for each individual eigenstate and to study its eigenstate-to-eigenstate fluctuations governed by the correlation length exponent ν . The scaling properties of critical eigenstates are also expected to appear much more clearly if one considers each eigenstate at its finite-size-pseudo-critical point, where it is ‘truly critical’, while standard averages over eigenstates and samples in the critical region actually see a mixture of states that are effectively either localized or delocalized.Abstract To understand the finite-size-scaling properties of phases transitions in classical and quantum models in the presence of quenched disorder, it has proven to be fruitful to introduce the notion of a finite-size-pseudo-critical point in each disordered sample and to analyze its sample-to-sample fluctuations as a function of the size. For the many-body-localization transition, where very strong eigenstate-to-eigenstate fluctuations have been numerically reported even within a given disordered sample at a given energy density (Yu, Luitz and Clark 2016 arXiv: 1606.01260 and Khemani, Lim, Sheng and Huse 2016 arXiv: 1607.05756 ), it seems thus useful to introduce the notion of a finite-size-pseudo-critical point for each individual eigenstate and to study its eigenstate-to-eigenstate fluctuations governed by the correlation length exponent ν . The scaling properties of critical eigenstates are also expected to appear much more clearly if one considers each eigenstate at its finite-size-pseudo-critical point, where it is ‘truly critical’, while standard averages over eigenstates and samples in the critical region actually see a mixture of states that are effectively either localized or delocalized.

arXiv:1606.07590Journal of Statistical Mechanics Theory and ExperimentDec 1, 20163 citations

NONUNIVERSAL FINITE-SIZE EFFECTS NEAR CRITICAL POINTS

V. Dohm

International Conference on Path IntegralsNov 1, 20080 citations

Scaling Theory for Finite-Size Effects in the Critical Region

Michael Ellis Fisher, Michael N. Barber

Current physics sources and commentsJan 1, 19882 citations

We study the role of finite-size effects on critical behavior near a metallic

q=0

critical point and compare the results with a recent extensive quantum Monte Carlo (QMC) study [Y. Schattner et al., Phys. Rev. X 6, 031028 (2016)]. This study found several features in both bosonic and fermionic responses, in disagreement with the expected critical behavior with a dynamical exponent

z=3

. We show that finite-size effects are particularly strong for

z=3

criticality and give rise to a behavior different from that of an infinite system, over a wide range of momenta and frequencies. We argue that by taking finite-size effects into account, the QMC results can be explained within

z=3

theory.