Finite size effects in the presence of a chemical potential: A study in the classical nonlinear O(2) sigma model

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2010-06-08

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Abstract

In the presence of a chemical potential, the physics of level crossings leads to singularities at zero temperature, even when the spatial volume is finite. These singularities are smoothed out at a finite temperature but leave behind nontrivial finite size effects which must be understood in order to extract thermodynamic quantities using Monte Carlo methods, particularly close to critical points. We illustrate some of these issues using the classical nonlinear O(2) sigma model with a coupling β and chemical potential μ on a 2+1-dimensional Euclidean lattice. In the conventional formulation this model suffers from a sign problem at nonzero chemical potential and hence cannot be studied with the Wolff cluster algorithm. However, when formulated in terms of the worldline of particles, the sign problem is absent, and the model can be studied efficiently with the "worm algorithm." Using this method we study the finite size effects that arise due to the chemical potential and develop an effective quantum mechanical approach to capture the effects. As a side result we obtain energy levels of up to four particles as a function of the box size and uncover a part of the phase diagram in the (β,μ) plane. © 2010 The American Physical Society.

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10.1103/PhysRevD.81.125007

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Banerjee, D, and S Chandrasekharan (2010). Finite size effects in the presence of a chemical potential: A study in the classical nonlinear O(2) sigma model. Physical Review D - Particles, Fields, Gravitation and Cosmology, 81(12). p. 125007. 10.1103/PhysRevD.81.125007 Retrieved from https://hdl.handle.net/10161/4275.

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Scholars@Duke

Chandrasekharan

Shailesh Chandrasekharan

Professor of Physics

Prof. Chandrasekharan is interested in understanding quantum field theories non-perturbatively from first principles calculations. His research focuses on lattice formulations of these theories with emphasis on strongly correlated fermionic systems of interest in condensed matter, particle and nuclear physics. He develops novel Monte-Carlo algorithms to study these problems. He is particularly excited about solutions to the notoriously difficult sign problem that haunts quantum systems containing fermions and gauge fields. He has proposed an idea called the fermion bag approach, using which he has been able to solve numerous sign problems that seemed unsolvable earlier. Using various algorithmic advances over the past decade, he is interested in understanding the properties of quantum critical points containing interacting fermions. Some of his recent publications can be found here. Recently he is exploring how one can use quantum computers to solve quantum field theories. 


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