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Quantum Systems and Critical Phenomena

Giovanni Battimelli, Giovanni Ciccotti, Pietro Greco

The frontiers collectionJan 1, 20200 citations

The critical behaviour of the 1-dimensional XY model with power law decay long range interactions

Masahiro Takamoto, Yoshinori Muraoka, Toshihiro Idogaki

We discuss the critical behaviour of the 1-dimensional classical XY model with power law decay long range interactions by using Monte Carlo simulation. It has been predicted by renormalization group calculation that the critical behaviour changes with the power of interactions. From the simulation result of temperature dependence of the specific heat, we confirm that the system shows the critical behaviour of the mean field type and the non-trivial long range order. We also estimate the critical exponent η for the system with the inverse square long range interactions, and by using the phenomenological renormalization group plot, we confirm the 'Berezinskii-Kosterlitz-Thouless (BKT)-like' transition which has been predicted by the spin wave calculations.We discuss the critical behaviour of the 1-dimensional classical XY model with power law decay long range interactions by using Monte Carlo simulation. It has been predicted by renormalization group calculation that the critical behaviour changes with the power of interactions. From the simulation result of temperature dependence of the specific heat, we confirm that the system shows the critical behaviour of the mean field type and the non-trivial long range order. We also estimate the critical exponent η for the system with the inverse square long range interactions, and by using the phenomenological renormalization group plot, we confirm the 'Berezinskii-Kosterlitz-Thouless (BKT)-like' transition which has been predicted by the spin wave calculations.

Journal of Physics Conference SeriesJan 1, 20101 citation

Scaling Theory of Quantum Critical Phenomena

World Scientific lecture notes in physicsJan 1, 20010 citations

Power-law-exponential interaction induced quantum spiral phases

Guoqing Tian, Ying Nian Wu, Xin‐You Lü

We theoretically predict a kind of power-law-exponential (PLE) dipole-dipole interaction between quantum emitters in a 1D waveguide QED system. This unconventional long-range interaction is the combination of power-law growth and exponential decay couplings. Applying the PLE interaction to a spin model, we uncover the rich many-body phases. Most remarkably, we find that the PLE interaction can induce the ordered and critical spiral phases. These spiral phases emerge from the strong frustration generated by the power-law factor of the PLE interaction; hence they are absent for other types of long-range interaction, e.g., pure exponential and power-law decay interactions. Our work is also applicable for the higher-dimensional systems. It fundamentally broadens the realm of many-body physics and has significant applications in quantum simulation of strongly correlated matter. Published by the American Physical Society 2024We theoretically predict a kind of power-law-exponential (PLE) dipole-dipole interaction between quantum emitters in a 1D waveguide QED system. This unconventional long-range interaction is the combination of power-law growth and exponential decay couplings. Applying the PLE interaction to a spin model, we uncover the rich many-body phases. Most remarkably, we find that the PLE interaction can induce the ordered and critical spiral phases. These spiral phases emerge from the strong frustration generated by the power-law factor of the PLE interaction; hence they are absent for other types of long-range interaction, e.g., pure exponential and power-law decay interactions. Our work is also applicable for the higher-dimensional systems. It fundamentally broadens the realm of many-body physics and has significant applications in quantum simulation of strongly correlated matter. Published by the American Physical Society 2024

arXiv:2405.14243Physical Review ResearchSep 12, 20245 citations

Critical behaviour of dissipative quantum systems

Alejandro Muramatsu, F. Guinea, Vincent Hakim

Advances in Solid State PhysicsSep 10, 20070 citations

Finite-size scaling investigations in the quantum varphi4-model with long-range interaction

Hassan Chamati, N. S. Tonchev

In this paper, we study in detail the critical behaviour of the ( n ) quantum 4 -model with long-range interaction decaying with distances r by a power law as r - d - in the large- n limit. The zero-temperature critical behaviour is discussed. Its alteration by finite temperature and/or finite sizes in the space is studied. The scaling behaviours are studied in different regimes depending upon whether the finite temperature or the finite sizes of the system lead. A number of results for the correlation length, critical amplitudes and the finite-size shift, for different dimensionalities between the lower d < = /2 and the upper d > = 3 /2 critical dimensions, are calculated.In this paper, we study in detail the critical behaviour of the ( n ) quantum 4 -model with long-range interaction decaying with distances r by a power law as r - d - in the large- n limit. The zero-temperature critical behaviour is discussed. Its alteration by finite temperature and/or finite sizes in the space is studied. The scaling behaviours are studied in different regimes depending upon whether the finite temperature or the finite sizes of the system lead. A number of results for the correlation length, critical amplitudes and the finite-size shift, for different dimensionalities between the lower d < = /2 and the upper d > = 3 /2 critical dimensions, are calculated.

arXiv:cond-mat/9910508Journal of Physics A Mathematical and GeneralFeb 1, 200015 citations

Unconventional critical behaviour in quantum systems with interactions decaying as a power law

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