Quantum critical phenomena of Bose-Hubbard model in three dimensions

Strong-to-weak spontaneous symmetry breaking has emerged as a novel form of ordering in monitored and open quantum systems, yet its characterization has so far primarily relied on nonlocal diagnostics. Here, we develop a Gutzwiller mean-field framework for monitored bosonic lattice systems, enabling the direct simulation of stochastic measurement dynamics in three spatial dimensions. Applying this approach to the monitored Bose-Hubbard model with local density measurements and Lindbladian dissipation, we identify strong-to-weak symmetry breaking through a trajectory-averaged local order parameter. We find that this local order parameter becomes critical near the critical measurement strength as the charge-sharpening transition. Both transitions exhibit a dynamical exponent $z=2$ in the dilute limit with a correlation length $ν\simeq 0.6$ , comparable to that of the charge-sharpening transition, suggesting that the two phenomena may originate from a common underlying critical point. Our work shows a local characterization of strong-to-weak symmetry breaking, reveals its connection to charge sharpening, and provides concrete predictions for future experiments on the monitored Bose-Hubbard model.Strong-to-weak spontaneous symmetry breaking has emerged as a novel form of ordering in monitored and open quantum systems, yet its characterization has so far primarily relied on nonlocal diagnostics. Here, we develop a Gutzwiller mean-field framework for monitored bosonic lattice systems, enabling the direct simulation of stochastic measurement dynamics in three spatial dimensions. Applying this approach to the monitored Bose-Hubbard model with local density measurements and Lindbladian dissipation, we identify strong-to-weak symmetry breaking through a trajectory-averaged local order parameter. We find that this local order parameter becomes critical near the critical measurement strength as the charge-sharpening transition. Both transitions exhibit a dynamical exponent $z=2$ in the dilute limit with a correlation length $ν\simeq 0.6$, comparable to that of the charge-sharpening transition, suggesting that the two phenomena may originate from a common underlying critical point. Our work shows a local characterization of strong-to-weak symmetry breaking, reveals its connection to charge sharpening, and provides concrete predictions for future experiments on the monitored Bose-Hubbard model.

cond-mat.quant-gasCross-listedarXiv:2606.02713Jun 3, 20260 citations

Quantum criticality in the two-dimensional Hubbard model

Mathias Pelz

Jul 10, 20260 citations

Finite-size scaling for quantum criticality above the upper critical dimension: Superfluid–Mott-insulator transition in three dimensions

Yasuyuki Kato, Naoki Kawashima

The validity of modified finite-size scaling above the upper critical dimension is demonstrated for the quantum phase transition whose dynamical critical exponent is z=2. We consider the N -component Bose-Hubbard model, which is exactly solvable and exhibits mean-field type critical phenomena in the large- N limit. The modified finite-size scaling holds exactly in that limit. However, the usual procedure, taking the large system-size limit with fixed temperature, does not lead to the expected (and correct) mean-field critical behavior because of the limited range of applicability of the finite-size scaling form. By quantum Monte Carlo simulation, it is shown that the modified finite-size scaling holds in the case of N=1.The validity of modified finite-size scaling above the upper critical dimension is demonstrated for the quantum phase transition whose dynamical critical exponent is z=2. We consider the N -component Bose-Hubbard model, which is exactly solvable and exhibits mean-field type critical phenomena in the large- N limit. The modified finite-size scaling holds exactly in that limit. However, the usual procedure, taking the large system-size limit with fixed temperature, does not lead to the expected (and correct) mean-field critical behavior because of the limited range of applicability of the finite-size scaling form. By quantum Monte Carlo simulation, it is shown that the modified finite-size scaling holds in the case of N=1.

arXiv:0910.0082Physical Review EJan 19, 20107 citations

Quantum Criticality and Dynamics in Two-dimensional Bose Gases

Xibo Zhang, Li-Chung Ha, Chen-Lung Hung +2 more

Bulletin of the American Physical SocietyJun 8, 20120 citations

Quantum Critical Phenomena

Yuto Ashida

Quantum critical phenomena originate from collective behavior of strongly correlated particles and lie at the heart of universal low-energy properties in many-body systems. The strong correlation between quantum particles is particularly prominent in a low-dimensional system. In the first part of this Chapter, we identify what types of measurements are relevant to one-dimensional low-energy properties and address how they qualitatively alter the underlying quantum critical behavior. In the second part, we study how the measurement backaction influences on quantum phase transitions in higher dimensions by focusing on the Bose-Hubbard model. For all the theoretical considerations, we discuss possible experimental implementations in ultracold atomic gases.Quantum critical phenomena originate from collective behavior of strongly correlated particles and lie at the heart of universal low-energy properties in many-body systems. The strong correlation between quantum particles is particularly prominent in a low-dimensional system. In the first part of this Chapter, we identify what types of measurements are relevant to one-dimensional low-energy properties and address how they qualitatively alter the underlying quantum critical behavior. In the second part, we study how the measurement backaction influences on quantum phase transitions in higher dimensions by focusing on the Bose-Hubbard model. For all the theoretical considerations, we discuss possible experimental implementations in ultracold atomic gases.

Springer thesesJan 1, 20200 citations

z=2

in the dilute limit with a correlation length

ν\simeq 0.6

, comparable to that of the charge-sharpening transition, suggesting that the two phenomena may originate from a common underlying critical point. Our work shows a local characterization of strong-to-weak symmetry breaking, reveals its connection to charge sharpening, and provides concrete predictions for future experiments on the monitored Bose-Hubbard model.