Mario Motta — Università di Milano # 
Dynamical response functions of the 2D electron gas from Auxiliary Fields Quantum Monte Carlo calculations # 

Quantum Monte Carlo (QMC) simulations of many body fermionic 
systems are considerably complicated by the well known sign problem [1]. Although very accurate approximation 
schemes have been developed for the calculation of static properties, the possibility of extending such 
methodologies to the investigation of dynamical properties is still largely unexplored [2]. Recently, a number 
of innovative QMC methods have been conceived, which map the imaginary time evolution into a random walk in the 
manifold of Slater determinants. In such methods the sign problem emerges in a different form, and can be 
treated introducing approximations that are more likely to permit the study of excited states [5]. We have 
focused on the phaseless auxiliary Fields QMC method (AFQMC), developed by S. Zhang [3]. Generalizing the formal 
manipulations suggested by F. Assaad et al. [4], we propose a practical scheme to evaluate dynamic correlation 
functions in imaginary time, giving access to the response functions of interacting fermionic systems. We assess 
the accuracy of the methodology via the study of exactly solvable simple models, comparing AFQMC predictions 
with exact solutions [5]. We also compute the imaginary time correlation functions and the effective mass of the 
two-dimensional homogeneous electron gas in the high-density regime, providing comparison between AFQMC and 
recent experimental data [6].
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REFERENCES:
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[1] R.P. Feynman, A.R. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill (1965) <br/>
[2] M. Nava, D. Galli, S. Moroni and E. Vitali:  arXiv:1302.1799 (2013) <br/>
[3] S. Zhang: 'Quantum Monte Carlo Methods for Strongly Correlated Electron Systems',
    in Theoretical Methods for Strongly Correlated Electron Systems, Springer Verlag (2003) <br/>
[4] M. Feldbacher and F. F. Assaad: Phys. Rev. B 63, 073105 (2001) <br/>
[5] M. Motta, D.E. Galli, S. Moroni and E. Vitali, J Chem Phys. 140, 024107 (2014) <br/>
[6] M. Motta, D.E. Galli, S. Moroni and E. Vitali, in preparation  <br/>