Rubem Mondaini (CSRC)
Hamming Distance and the onset of quantum criticality 

Simulating models for quantum correlated matter unveils the inherent limitations of deterministic classical computations. In particular, in the case of quantum Monte Carlo methods, this is manifested by the emergence of negative weight configurations in the sampling, that is, the sign problem (SP). There have been several recent calculations which exploit the SP to locate underlying critical behavior [1, 2, 3]. In this talk, I plan to show that by utilizing a metric that quantifies phase-space ergodicity in such sampling, the Hamming distance, a significant advance on these ideas to extract the location of quantum critical points in various fermionic models is obtained, in spite of the presence of a severe SP. Combined with other methods, exact diagonalization in our case, it elucidates both the nature of the different phases as well as their location, as we demonstrate explicitly for the honeycomb and triangular Hubbard models, in both their U(1) and SU(2) forms. By directly tackling properties of the auxiliary-fields, our approach exemplifies a possible path to circumvent inherent limitations imposed by the SP, allowing the exploration of the phase diagram of a variety of fermionic quantum models hitherto considered to be impractical via quantum Monte Carlo simulations [4]. 

[1] Quantum critical points and the sign problem, R. Mondaini, S. Tarat, R Scalettar, Science 375, 418 (2022) 
[2] Universality and Critical Exponents of the Fermion Sign Problem, R. Mondaini, S. Tarat, R. Scalettar, submitted (2022) 
[3] Deconvolving the components of the sign problem S. Tarat, B. Xiao, R. Mondaini, R. Scalettar Physical Review B 105, 045107 (2022) 
[4] Hamming Distance and the onset of quantum criticality, T. Yi, R. Scalettar, R. Mondaini arXiv preprint, arXiv:2111.12936