Hamming Distance and the onset of quantum criticality

Yi, Tian-Cheng; Scalettar, Richard; Mondaini, Rubem

doi:10.48550/arxiv.2111.12936

Cited by 3 publications

(5 citation statements)

References 53 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…i,τ } is a 'typical' configuration (namely, one obtained after a significant number of warmup sweeps in the field), storing HD after each sweep on the sampling allows one to quantify the average distance the Markov chain probes in the (d + 1)-dimensional phase space. This was shown to be intrinsically related to the physics of the models being investigated [36]. For example, unordered phases were demonstrated to be associated with completely uncorrelated HS configurations, rendering an average Hamming distance, HD, equals to 0.5.…”

Section: ŝZmentioning

confidence: 93%

“…Hamming Distance.-Recent investigations in various fermionic models have shown that the onset of criticality can be directly tracked by quantities related to metrics of the auxiliary Hubbard-Stratonovich (HS) field [36,55], bypassing the necessity of extraction of physical observables. This field, local to each orbital in the spinful Hubbard model in its (d + 1)-dimensions formulation [22], is the quantity being sampled via a Metropolis algorithm over the course of the Monte Carlo sampling [23].…”

Section: ŝZmentioning

confidence: 99%

“…Such saturation is also seen in quantifiers of the typically sampled fields in DQMC, e.g. the average Hamming distance [26,36]. Although a scaling analysis based on the average sign of the weights S σ [24] is elusive, likely due to the absence of an intrinsic order parameter characterizing either phase, other models where a band-insulating phase takes place, as the square lattice ionic Hubbard model [37][38][39][40][41], also exhibit a convergence of S σ towards one, as we similarly observe here [11,24].…”

mentioning

confidence: 99%

See 2 more Smart Citations

Bilayer Hubbard model: Analysis based on the fermionic sign problem

Mou,

Mondaini,

Scalettar

2022

Preprint

Self Cite

View full text Add to dashboard Cite

The bilayer Hubbard model describes the antiferromagnet to spin singlet transition and, potentially, aspects of the physics of unconventional superconductors. Despite these important applications, significant aspects of its 'phase diagram' in the interplane hopping t ⊥ vs. on-site interaction U parameter space, at half-filling, are largely in disagreement. Here we provide a novel analysis making use of the average sign of weights over the course of the importance sampling in quantum Monte Carlo simulations to resolve several central open questions. Specifically, this metric of the weights clarifies the finite-sized metallic regimes at small U . Furthermore, at strong interactions, it points to the existence of a crossover from a correlated to uncorrelated band-insulator not yet explored in a variety of existing, unbiased numerical methods. Our work demonstrates the versatility of using properties of the weights in quantum Monte Carlo simulations to reveal important physical characteristics of the models under study.

show abstract

Section: ŝZmentioning

confidence: 93%

Section: ŝZmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Bilayer Hubbard model: Analysis based on the fermionic sign problem

Mou,

Mondaini,

Scalettar

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Accordingly, we propose a greedy approach to compute the Tikhonov regularization term based on Hamming distance efficiently. In the context of dealing with binary values: 0 or 1, Hamming distance between two-bit vectors of equal lengths is the number of bits at which the corresponding elements of the vectors have different values and can be represented as follows [46]:…”

Section: Hamming-based Tikhonov Regularization Approachmentioning

confidence: 99%

A power-aware task scheduler for energy harvesting-based wearable biomedical systems using snake optimizer

Yousri

Elbayoumi

Soltan

et al. 2023

Analog Integr Circ Sig Process

View full text Add to dashboard Cite

There is an increasing interest in energy harvesting for wearable biomedical devices. This requires power conservation and management to ensure long-term and steady operation. Hence, task scheduling algorithms will be used throughout this work to provide a reliable solution to minimize energy consumption while considering the system operation constraints. This study proposes a novel power-aware task scheduler to manage system operations. For example, we used the scheduler to handle system operations, including heart rate and temperature sensors. Two optimization techniques have been used to illustrate the impact of task scheduling on energy consumption. The first is based on Snake Optimizer (SO), and the second is a greedy approach to compute the Hamming-based Tikhonov regularization. The FPA approach showed 50$$\%$$ % improvement in the convergence time for the scheduler.

show abstract

“…There also exists suggestion that the negative sign of a configuration is a topological invariant, which is an imaginary time counterpart of the Aharonov-Anandan phase and can be reduced to a Berry phase in the adiabatic limit [39]. Moreover, it was shown recently that some interacting models may have intrinsic sign problem, which cannot be cured regardless [40][41][42][43], and the sign problem has even been linked to quantum phase transitions [44][45][46].…”

mentioning

confidence: 99%

Fermion sign bounds theory in quantum Monte Carlo simulation

Zhang,

Pan,

et al. 2021

Preprint

View full text Add to dashboard Cite

Sign problem in quantum Monte Carlo (QMC) simulation appears to be an extremely hard problem. Traditional lore passing around for years tells people that when there is a sign problem, the average sign in QMC simulation approaches zero exponentially fast with the space-time volume of the configurational space. We, however, show this is not always the case and manage to find bounds for the sign problem. Our new understanding is based on a direct connection between the sign problem bounds and ground state properties on finite size and could distinguish when the bounds have the usual exponential scaling, and when they are bestowed on an algebraic scaling. We show such algebraic sign problems in fermionic QMC for quantum Moiré lattice models both in real and momentum space at low temperature limit. Our approach inspires new ways to cure, ease and even make use of the sign problem.

show abstract

Hamming Distance and the onset of quantum criticality

Cited by 3 publications

References 53 publications

Bilayer Hubbard model: Analysis based on the fermionic sign problem

Bilayer Hubbard model: Analysis based on the fermionic sign problem

A power-aware task scheduler for energy harvesting-based wearable biomedical systems using snake optimizer

Fermion sign bounds theory in quantum Monte Carlo simulation

Contact Info

Product

Resources

About