Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session N43: The Quantum Monte Carlo Sign Problem: Recent Advances and Paths ForwardInvited Live Streamed

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Sponsoring Units: DCOMP Chair: Itay Hen, University of Southern California Room: McCormick Place W375B 
Wednesday, March 16, 2022 11:30AM  12:06PM 
N43.00001: Overcoming the quantum sign problem Invited Speaker: Dominik Hangleiter The infamous socalled 'sign problem' is responsible for the computational intractability of predicting features of many quantum systems via Monte Carlo algorithms on the one hand, and facilitates the power of quantum computing devices on the other hand. In my talk, I will present various perspectives and results on the quantum sign problem, with the goal to overcome the limitations it poses to predicting properties of physical systems. In particular, I will discuss the possibility of systematically mitigating the sign problem of Monte Carlo algorithms. I close with an outlook onto using precisely controlled quantum simulators to predict properties of quantum materials and discuss some challenges we face when improving their accuracy. 
Wednesday, March 16, 2022 12:06PM  12:42PM 
N43.00002: Intrinsic sign problems in topological quantum field theories Invited Speaker: Zohar Ringel The sign problem is a widespread numerical hurdle preventing us from simulating the equilibrium behaviour of many interesting models, most notably the Hubbard model. Research aimed at solving the sign problem, via various clever manipulations, has been thriving for a long time with various recent exciting results. The complementary question, of whether some phases of matter forbid the existence of any signfree microscopic model, has received attention only recently. In this talk, I'll review recent progress and discuss a novel, and quite general, criterion we obtained for when a topological quantum field theory (TQFT) has no signfree local microscopic model. Most but not all TQFTs test positive under this criterion. Relations to sign problems in frustrated magnets will also be discussed. 
Wednesday, March 16, 2022 12:42PM  1:18PM 
N43.00003: Entanglement Structure in Stoquastic Frustration Free Ground States Invited Speaker: Elizabeth Crosson The wellknown similarity transformation between the generators of Glauber dynamics for classical spin systems and quantum Hamiltonians gives rise to a variety of exactly solvable models without a sign problem, such as the quantum dimer model at the RokhsarKivelson critical point. In this talk we describe a partial converse of this mapping, deriving sufficient conditions for stoquastic frustration free (SFF) ground states to be coherent classical Gibbs states with a local energy function. This leads to a decomposition of general SFF ground state entanglement into shortrange contributions from the local energy function, and longrange entanglement from global constraints (such as conservation of parity or charge). From this perspective we can see the sign problem, and the associated phase frustration in the ground state wave function, is itself a primary mechanism for longrange entanglement in general quantum ground states. 
Wednesday, March 16, 2022 1:18PM  1:54PM 
N43.00004: Fermionic sign problem: an exaggerated myth Invited Speaker: Nikolay Prokofiev Feynman diagrams are the most celebrated and powerful tool of theoretical physics usually associated with an analytic approach. I will argue that diagrammatic expansions are also an ideal numerical tool with enormous and yet to be explored potential for solving interacting fermionic systems by direct simulation of connected Feynman diagrams. Though the original series based on bare propagators and interaction vertexes are signalternating and often divergent one can determine the answer behind them by using appropriate series resummation techniques, conformal mappings, asymptotic series analysis, and shifted action tools, including sequences based on the skeleton diagrams. Ultimately, the diagrammatic expansion can, in principle, be always made convergent! In this formulation, the fermionic sign problem is simply absent for regular (as opposed to random) systems because (i) the entire setup is valid in the thermodynamic limit, and (ii) convergence to the exact answer is polynomial in time. Moreover, the fermionic sign is a "blessing" because it leads to massive cancellation of highorder diagrams and ultimate convergence of the resummed series. For illustration, I will discuss results for the FermiHubbard model, the unitary Fermi gas, and the homogeneous electron gas (jellium). 
Wednesday, March 16, 2022 1:54PM  2:30PM 
N43.00005: The sign problem, nonstoquasticity and everything in between Invited Speaker: Itay Hen The quantum Monte Carlo sign problem has been rightfully recognized as one of the grand challenges of computational physics. This problem encapsulates our inability to develop a proper understanding of many important quantum manybody phenomena in physics, chemistry and well beyond. Despite its centrality, the circumstances under which the sign problem arises or can be resolved as well as its interplay with the related notion of `nonstoquasticity' are often not very well understood. In this talk, I will attempt to elucidate the circumstances under which the sign problem emerges and clear up some of the confusion surrounding this intricate computational phenomenon. Making use of the recently introduced offdiagonal series expansion quantum Monte Carlo technique, I will discuss a sufficient and necessary condition for the simulability of quantum manybody Hamiltonians and provide a construction for nonstoquastic, yet signproblemfree and hence QMCsimulable, quantum manybody models. 
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