In the face of mounting numerical evidence, Metlitski and Grover (arXiv:1112.5166) have given compelling analytical arguments that systems with spontaneous broken continuous symmetry contain a subleading contribution to the entanglement entropy that diverges logarithmically with system size. They predict that the coefficient of this log is a universal quantity that depends on the number of Goldstone modes. In this paper, we confirm the presence of this log term through quantum Monte Carlo calculations of the second R\'enyi entropy on the spin-1/2 $XY$ model. Devising an algorithm to facilitate convergence of entropy data at extremely low temperatures, we demonstrate that the single Goldstone mode in the ground state can be identified through the coefficient of the log term. Furthermore, our simulation accuracy allows us to obtain an additional geometric constant additive to the R\'enyi entropy, that matches a predicted fully universal form obtained from a free bosonic field theory with no adjustable parameters.In the face of mounting numerical evidence, Metlitski and Grover (arXiv:1112.5166) have given compelling analytical arguments that systems with spontaneous broken continuous symmetry contain a subleading contribution to the entanglement entropy that diverges logarithmically with system size. They predict that the coefficient of this log is a universal quantity that depends on the number of Goldstone modes. In this paper, we confirm the presence of this log term through quantum Monte Carlo calculations of the second R\'enyi entropy on the spin-1/2 $XY$ model. Devising an algorithm to facilitate convergence of entropy data at extremely low temperatures, we demonstrate that the single Goldstone mode in the ground state can be identified through the coefficient of the log term. Furthermore, our simulation accuracy allows us to obtain an additional geometric constant additive to the R\'enyi entropy, that matches a predicted fully universal form obtained from a free bosonic field theory with no adjustable parameters.

arXiv:1502.01722Physical Review BSep 25, 201540 citations

Extracting universal corner entanglement entropy during the quantum Monte Carlo simulation

Yuan Da Liao, Menghan Song, Jiarui Zhao +1 more

The subleading corner logarithmic corrections in entanglement entropy (EE) are crucial for revealing the universal characteristics of quantum critical points (QCPs), but they are challenging to detect. Motivated by recent developments in the stable computation of EE in ( $2+1$ )-dimensional [( $2+1$ )D] quantum many-body systems, we have developed a method for directly measuring the corner contribution in EE with lower computational cost. The cornerstone of our approach is to measure the subtracted corner entanglement entropy (SCEE), defined as the difference between the EEs of subregions with the same boundary length for smooth and cornered boundaries during a sign-problem-free quantum Monte Carlo simulation. Our improved method inherently eliminates not only the area-law term of EE but also the subleading log corrections arising from Goldstone modes, leaving the universal corner contribution as the leading term of the SCEE with greatly improved data quality. Utilizing this advanced approach, we calculate the SCEE of the bilayer Heisenberg model on both square and honeycomb lattices across their ( $2+1$ )D $O$ (3) QCPs with different opening angles on the entanglement boundary and obtain accurate values of the corresponding universal corner log coefficients. These findings will encourage further theoretical investigations to access controlled universal information for interacting conformal field theories at ( $2+1$ ) dimensions.The subleading corner logarithmic corrections in entanglement entropy (EE) are crucial for revealing the universal characteristics of quantum critical points (QCPs), but they are challenging to detect. Motivated by recent developments in the stable computation of EE in ($2+1$)-dimensional [($2+1$)D] quantum many-body systems, we have developed a method for directly measuring the corner contribution in EE with lower computational cost. The cornerstone of our approach is to measure the subtracted corner entanglement entropy (SCEE), defined as the difference between the EEs of subregions with the same boundary length for smooth and cornered boundaries during a sign-problem-free quantum Monte Carlo simulation. Our improved method inherently eliminates not only the area-law term of EE but also the subleading log corrections arising from Goldstone modes, leaving the universal corner contribution as the leading term of the SCEE with greatly improved data quality. Utilizing this advanced approach, we calculate the SCEE of the bilayer Heisenberg model on both square and honeycomb lattices across their ($2+1$)D $O$(3) QCPs with different opening angles on the entanglement boundary and obtain accurate values of the corresponding universal corner log coefficients. These findings will encourage further theoretical investigations to access controlled universal information for interacting conformal field theories at ($2+1$) dimensions.

arXiv:2404.13876Physical review. B./Physical review. BDec 3, 20246 citations

Quantum Monte Carlo Calculations of Entanglement

Norm M. Tubman, Jeremy McMinis

Bulletin of the American Physical SocietyMar 22, 20130 citations

XY

model. Devising an algorithm to facilitate convergence of entropy data at extremely low temperatures, we demonstrate that the single Goldstone mode in the ground state can be identified through the coefficient of the log term. Furthermore, our simulation accuracy allows us to obtain an additional geometric constant additive to the R\'enyi entropy, that matches a predicted fully universal form obtained from a free bosonic field theory with no adjustable parameters.

2+1

)-dimensional [(

2+1

)D] quantum many-body systems, we have developed a method for directly measuring the corner contribution in EE with lower computational cost. The cornerstone of our approach is to measure the subtracted corner entanglement entropy (SCEE), defined as the difference between the EEs of subregions with the same boundary length for smooth and cornered boundaries during a sign-problem-free quantum Monte Carlo simulation. Our improved method inherently eliminates not only the area-law term of EE but also the subleading log corrections arising from Goldstone modes, leaving the universal corner contribution as the leading term of the SCEE with greatly improved data quality. Utilizing this advanced approach, we calculate the SCEE of the bilayer Heisenberg model on both square and honeycomb lattices across their (

2+1

O

(3) QCPs with different opening angles on the entanglement boundary and obtain accurate values of the corresponding universal corner log coefficients. These findings will encourage further theoretical investigations to access controlled universal information for interacting conformal field theories at (

2+1

) dimensions.