Entanglement at a two-dimensional quantum critical point: a T = 0 projector quantum Monte Carlo study

نویسندگان

  • Roger G Melko
  • Stephen Inglis
چکیده

Although the leading-order scaling of entanglement entropy is nonuniversal at a quantum critical point (QCP), sub-leading scaling can contain universal behaviour. Such universal quantities are commonly studied in noninteracting field theories, however it typically requires numerical calculation to access them in interacting theories. In this paper, we use large-scale T = 0 quantum Monte Carlo simulations to examine in detail the second Rényi entropy of entangled regions at the QCP in the transverse-field Ising model in 2 + 1 space–time dimensions—a fixed point for which there is no exact result for the scaling of entanglement entropy. We calculate a universal coefficient of a vertexinduced logarithmic scaling for a polygonal entangled subregion, and compare the result to interacting and non-interacting theories. We also examine the shapedependence of the Rényi entropy for finite-size toroidal lattices divided into two entangled cylinders by smooth boundaries. Remarkably, we find that the dependence on cylinder length follows a shape-dependent function calculated previously by Stephan et al (2013 New J. Phys. 15 015004) at the QCP corresponding to the 2 + 1 dimensional quantum Lifshitz free scalar field theory. The quality of the fit of our data to this scaling function, as well as the apparent cutoff-independent coefficient that results, presents tantalizing evidence that this function may reflect universal behaviour across these and other very disparate QCPs in 2 + 1 dimensional systems. 3 Author to whom any correspondence should be addressed. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. New Journal of Physics 15 (2013) 073048 1367-2630/13/073048+24$33.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Critical Behavior and Griffiths-McCoy Singularities in the Two-Dimensional Random Quantum Ising Ferromagnet

We study the quantum phase transition in the two-dimensional random Ising model in a transverse field by Monte Carlo simulations. We find results similar to those known analytically in one dimension. At the critical point the dynamical exponent is infinite and the typical correlation function decays with a stretched exponential dependence on distance. Away from the critical point there are Grif...

متن کامل

ar X iv : c on d - m at / 9 61 21 81 v 1 1 9 D ec 1 99 6 MAGNETIC PROPERTIES OF THE 2 D t – t ′ – HUBBARD MODEL

The two–dimensional (2D) t–t’–Hubbard model is studied within the slave–boson (SB) theory. At half–filling, a paramagnetic to antiferromagnetic phase transition of first order at a finite critical interaction strength Uc(t /t) is found. The dependences on U/t and t/t of the sublattice magnetization and of the local magnetic moment are calculated. Our results reasonably agree with recent (Projec...

متن کامل

Evidence of Unconventional Universality Class in a Two-Dimensional Dimerized Quantum Heisenberg Model

The two-dimensional J-J ′ dimerized quantum Heisenberg model is studied on the square lattice by means of (stochastic series expansion) quantum Monte Carlo simulations as a function of the coupling ratio α = J /J . The critical point of the order-disorder quantum phase transition in the J-J ′ model is determined as αc = 2.5196(2) by finite-size scaling for up to approximately 10 000 quantum spi...

متن کامل

Estimation of Properties of Low-lying Excited States of Hubbard Models : a Multi-configurational Symmetrized Projector Quantum Monte Carlo Approach

We present in detail the recently developed multiconfigurational symmetrized-projector quantum Monte Carlo (MSPQMC) method for excited states of the Hubbard model. We describe the implementation of the Monte Carlo method for a multiconfigurational trial wavefunction. We give a detailed discussion of issues related to the symmetry of the projection procedure which validates our Monte Carlo proce...

متن کامل

Superfluid-insulator transition in the disordered two-dimensional Bose-Hubbard model

We investigate the superfluid-insulator transition in the disordered two-dimensional Bose-Hubbard model through quantum Monte Carlo simulations. The Bose-Hubbard model is studied in the presence of site disorder, and the quantum critical point between the Bose glass and superfluid is determined in the grand canonical ensemble at μ/U = 0 (close to ρ = 0.5), μ/U = 0.375 (close to ρ = 1), and μ/U ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2013