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Journal of the Physical Society of Japan

Quantum Simulation of Quantum Berezinskii–Kosterlitz–Thouless Transition for Interacting Light-Matter System: A Few Exact Results

Y R Kartik, Ranjith Kumar R, S Rahul, Sujit Sarkar

Published Oct 4, 2021• 0 citations
Publisher

Abstract

An attempt is made to understand the quantum simulation of quantum Berezinskii–Kosterlitz–Thouless (QBKT) transition for interacting light-matter system. We derive the QBKT equation for our system along with the exact results. We present emergence of different quantum phases in the different regimes of parameter space for this quantum simulated system. We interpret the collective excitations of the system in terms of bosonic excitations (Bose metal phase) as well as the photon blocked state (photonic insulator state) in our study. We present the behavior of renormalization group (RG) flow lines from the numerical studies of RG flow equations and also from the exact solution. We study the quantum critical surface of the simulated model Hamiltonian and also present the exact results for Majumdar–Ghosh point as well as for refermionization point from the perspective of quantum simulation.

DOI
10.7566/jpsj.90.114001

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The physics of the topological state of matter is the second revolution in quantum mechanics. We study the effect of interactions on the topological quantum phase transition and the quantum Berezinskii-Kosterlitz-Thouless (QBKT) transition in topological state of a quantum many-body condensed matter system. We predict a topological quantum phase transition from topological superconducting phase to an insulating phase for the interacting Kitaev chain. We observe interesting behaviour from the results of renormalization group study on the topological superconducting phase. We derive the renormalization group (RG) equation for QBKT through different routes with a few exact solutions along with the physical explanations, wherein we find the existence of two new important emergent phases apart from the two conventional phases of this model Hamiltonian. We also present results of a length-scale dependent study to predict asymptotic freedom like behaviour of the system. We do rigorous quantum field theoretical renormalization group calculations to solve this problem.
We present extensive calculation and the results of quantum Berezinskii-Kosterlitz-Thouless (BKT) transition for interacting helical liquid system. This system shows the quantum BKT transition for the different physical situation which we present by two model Hamiltonians. We derive the renormalization group (RG) equations explicitly and present the flow lines behavior. We also present RG flow lines based on the exact solution. We observe that the Majorana fermion zero modes physics and the gapped Ising phase of the system. We also observe that the evidence of gapless Luttinger liquid phase as a common phase for both quantum BKT transitions.
The Berezinskii-Kosterlitz-Thouless (BKT) mechanism governs the critical behavior of a wide range of many-body systems. We show here that this phenomenon is not restricted to conventional many body system but also for the strongly correlated parity-time (PT) symmetry quantum criticality. We show explicitly behaviour of topological excitation for the real and imaginary part of the potential are different through the analysis of second order and third order renormalization group (RG). One of the most interesting feature that we observe from our study the presence of hidden QBKT and also conventional QBKT for the real part of the potential whereas there is no such evidence for the imaginary part of the potential. We also present the exact solution for the RG flow lines. We show explicitly how the physics of single field double frequencies sine-Gordon Hamiltonian effectively transform to the dual field double frequencies sine-Gordon Hamiltonian for a certain regime of parameter space. This is the first example in any quantum many body systems. We present the results of second order and third order RG flow results explicitly for the real and imaginary part of the potential. This PT symmetric system can be experimentally tested in ultra-cold atoms. This work provides a new perspective for the PT symmetric quantum criticality.
We study the quantum phase transition of light of a system when atom trapped in microcavities and interacting through the exchange of virtual photons.We predict the quantum phase transition between the photonic Coulomb blocked induce insulating phase and anisotropic exchange induced photonic superfluid phase in the system due to the existence of two Rabi frequency oscillations.The renormalization group equation shows explicitly that for this system there is no self-duality.The system also shows two Berezinskii-Kosterlitz-Thouless (BKT) transitions for the different physical situation of the system.The presence of single Rabi frequency oscillation in the system leads to the BKT transition where system shows the quantum phase transition from photonic metallic state to the Coulomb blocked induced insulating phase.For the other BKT transition when the z-component of exchange interaction is absent, the system shows the transition from the photonic metallic state to the photonic superfluid phase.We also predict the commensurate to incommensurate transition under the laser field detuning.
We consider the interacting helical liquid system at the one-dimensional edge of a two-dimensional topological insulator, coupled to an external magnetic field and s-wave superconductor and map it to an XYZ spin chain system. This model undergoes quantum Berezinskii–Kosterlitz–Thouless (BKT) transition with two limiting conditions. We derive the renormalization group (RG) equations explicitly and also present the flow lines behavior. We also present the behavior of RG flow lines based on the exact solution. We observe that the physics of Majorana fermion zero modes and the gaped Ising-ferromagnetic phase, which appears in a different context. We observe that the evidence of gapless helical Luttinger liquid phase as a common non-topological quantum phase for both quantum BKT transitions. We explain analytically and physically that there is no Majorana-Ising transition. In the presence of chemical potential, the system shows the commensurate to incommensurate transition.