scholarly journals Unconventional quantum phase transition in the finite-size Lipkin–Meshkov–Glick model

2006 ◽  
Vol 8 (12) ◽  
pp. 297-297 ◽  
Author(s):  
Gang Chen ◽  
J-Q Liang
Keyword(s):  
Phase Transition ◽  
Quantum Phase Transition ◽  
Finite Size ◽  
Quantum Phase

scholarly journals Classical and Quantum Signatures of Quantum Phase Transitions in a (Pseudo) Relativistic Many-Body System

2020 ◽  
Vol 5 (2) ◽  
pp. 26
Author(s):  
Maximilian Nitsch ◽  
Benjamin Geiger ◽  
Klaus Richter ◽  
Juan-Diego Urbina
Keyword(s):  
Phase Transition ◽  
Quantum Phase Transition ◽  
Quantum Phase Transitions ◽  
Mean Field ◽  
Finite Size ◽  
Quantum Phase ◽  
Effective Model ◽  
Field Analysis ◽  
Many Body ◽  
Linear Dispersion

We identify a (pseudo) relativistic spin-dependent analogue of the celebrated quantum phase transition driven by the formation of a bright soliton in attractive one-dimensional bosonic gases. In this new scenario, due to the simultaneous existence of the linear dispersion and the bosonic nature of the system, special care must be taken with the choice of energy region where the transition takes place. Still, due to a crucial adiabatic separation of scales, and identified through extensive numerical diagonalization, a suitable effective model describing the transition is found. The corresponding mean-field analysis based on this effective model provides accurate predictions for the location of the quantum phase transition when compared against extensive numerical simulations. Furthermore, we numerically investigate the dynamical exponents characterizing the approach from its finite-size precursors to the sharp quantum phase transition in the thermodynamic limit.

scholarly journals Quantum discord and quantum phase transition in spin-1/2 frustrated Heisenberg chain

2013 ◽  
Vol 13 (5&6) ◽  
pp. 452-468
Author(s):  
Chu-Hui Fan ◽  
Heng-Na Xiong ◽  
Yixiao Huang ◽  
Zhe Sun
Keyword(s):  
Phase Transition ◽  
Quantum Phase Transition ◽  
Quantum Discord ◽  
Nearest Neighbor ◽  
Finite Size ◽  
Quantum Phase ◽  
Nonlinear Dependence ◽  
Heisenberg Chain ◽  
Transition Points ◽  
Analytical Result

By using the concept of the quantum discord (QD), we study the spin-1/2 antiferromagnetic Heisenberg chain with next-nearest-neighbor interaction. Due to the $SU(2)$ symmetry and $Z_{2}$ symmetry in this system, we obtain the analytical result of the QD and its geometric measure (GMQD), which is determined by the two-site correlators. For the 4-site and 6-site cases, the connection between GMQD (QD) and the eigenenergies was revealed. From the analytical and numerical results, we find GMQD (QD) is an effective tool in detecting the both the first-order and the infinite-order quantum-phase-transition points for the finite-size systems. Moreover, by using the entanglement excitation energy and a universal frustration measure we consider the frustration properties of the system and find a nonlinear dependence of the GMQD on the frustration.

scholarly journals Finite-size scaling of the photon-blockade breakdown dissipative quantum phase transition

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 150 ◽  
Author(s):  
A. Vukics ◽  
A. Dombi ◽  
J. M. Fink ◽  
P. Domokos
Keyword(s):  
Phase Transition ◽  
Thermodynamic Limit ◽  
Quantum Phase Transition ◽  
Finite Size ◽  
Quantum Phase ◽  
Finite Size Scaling ◽  
First Order ◽  
Size Scaling ◽  
First Order Phase Transition ◽  
Photon Blockade

We prove that the observable telegraph signal accompanying the bistability in the photon-blockade-breakdown regime of the driven and lossy Jaynes–Cummings model is the finite-size precursor of what in the thermodynamic limit is a genuine first-order phase transition. We construct a finite-size scaling of the system parameters to a well-defined thermodynamic limit, in which the system remains the same microscopic system, but the telegraph signal becomes macroscopic both in its timescale and intensity. The existence of such a finite-size scaling completes and justifies the classification of the photon-blockade-breakdown effect as a first-order dissipative quantum phase transition.

scholarly journals Adiabatic quenches and characterization of amplitude excitations in a continuous quantum phase transition

2016 ◽  
Vol 113 (34) ◽  
pp. 9475-9479 ◽  
Author(s):  
Thai M. Hoang ◽  
Hebbe M. Bharath ◽  
Matthew J. Boguslawski ◽  
Martin Anquez ◽  
Bryce A. Robbins ◽  
...  
Keyword(s):  
Phase Transition ◽  
Quantum Phase Transition ◽  
Energy Gap ◽  
Quantum Critical Point ◽  
Mean Field ◽  
Finite Size ◽  
Quantum Phase ◽  
Nonequilibrium Dynamics ◽  
Many Body ◽  
Goldstone Modes

Spontaneous symmetry breaking occurs in a physical system whenever the ground state does not share the symmetry of the underlying theory, e.g., the Hamiltonian. This mechanism gives rise to massless Nambu–Goldstone modes and massive Anderson–Higgs modes. These modes provide a fundamental understanding of matter in the Universe and appear as collective phase or amplitude excitations of an order parameter in a many-body system. The amplitude excitation plays a crucial role in determining the critical exponents governing universal nonequilibrium dynamics in the Kibble–Zurek mechanism (KZM). Here, we characterize the amplitude excitations in a spin-1 condensate and measure the energy gap for different phases of the quantum phase transition. At the quantum critical point of the transition, finite-size effects lead to a nonzero gap. Our measurements are consistent with this prediction, and furthermore, we demonstrate an adiabatic quench through the phase transition, which is forbidden at the mean field level. This work paves the way toward generating entanglement through an adiabatic phase transition.

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