Quantum Brownian Motion: proving that the Schmid transition belongs to the Berezinskii-Kosterlitz-Thouless universality class
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866915869714546688 |
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| author | Capone, Francesco G. de Candia, Antonio Cataudella, Vittorio Fazio, Rosario Nagaosa, Naoto Perroni, Carmine Antonio De Filippis, Giulio |
| author_facet | Capone, Francesco G. de Candia, Antonio Cataudella, Vittorio Fazio, Rosario Nagaosa, Naoto Perroni, Carmine Antonio De Filippis, Giulio |
| contents | We investigate the equilibrium properties of a quantum Brownian particle moving in a periodic potential, specifically addressing the nature of the dissipation-driven Schmid transition in the Ohmic regime. By employing World-Line Monte Carlo in the path-integral formalism and introducing a specific binary order parameter, we demonstrate that the transition belongs to the Berezinskii-Kosterlitz-Thouless universality class. This classification is substantiated through finite-size scaling analysis that reveals the characteristic logarithmic decay of the correlation functions associated with the order parameter at the critical point. Quantum phase transition turns out to be extremely fragile: it disappears in both over- and sub-Ohmic dissipation regimes. Crucially, we find that the presence of the periodic potential does not alter the localization properties in the sub-Ohmic and super-Ohmic regimes, where the system exhibits the same qualitative behavior as the free quantum Brownian particle. These findings highlight that the emergence of critical behavior is strictly governed by the low-frequency form of the environmental spectral function, which determines the long-range temporal decay of the dissipative kernel. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_16227 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum Brownian Motion: proving that the Schmid transition belongs to the Berezinskii-Kosterlitz-Thouless universality class Capone, Francesco G. de Candia, Antonio Cataudella, Vittorio Fazio, Rosario Nagaosa, Naoto Perroni, Carmine Antonio De Filippis, Giulio Statistical Mechanics Superconductivity Quantum Physics We investigate the equilibrium properties of a quantum Brownian particle moving in a periodic potential, specifically addressing the nature of the dissipation-driven Schmid transition in the Ohmic regime. By employing World-Line Monte Carlo in the path-integral formalism and introducing a specific binary order parameter, we demonstrate that the transition belongs to the Berezinskii-Kosterlitz-Thouless universality class. This classification is substantiated through finite-size scaling analysis that reveals the characteristic logarithmic decay of the correlation functions associated with the order parameter at the critical point. Quantum phase transition turns out to be extremely fragile: it disappears in both over- and sub-Ohmic dissipation regimes. Crucially, we find that the presence of the periodic potential does not alter the localization properties in the sub-Ohmic and super-Ohmic regimes, where the system exhibits the same qualitative behavior as the free quantum Brownian particle. These findings highlight that the emergence of critical behavior is strictly governed by the low-frequency form of the environmental spectral function, which determines the long-range temporal decay of the dissipative kernel. |
| title | Quantum Brownian Motion: proving that the Schmid transition belongs to the Berezinskii-Kosterlitz-Thouless universality class |
| topic | Statistical Mechanics Superconductivity Quantum Physics |
| url | https://arxiv.org/abs/2603.16227 |