scholarly journals Quantum phase transitions in nonhermitian harmonic oscillator

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Miloslav Znojil
Keyword(s):  
Phase Transition ◽  
Hilbert Space ◽  
Harmonic Oscillator ◽  
Quantum Phase Transitions ◽  
Quantum Phase ◽  
Dynamical Regime ◽  
Symmetric Version ◽  
Stable Quantum ◽  
Crossing Point ◽  
Stone Theorem

Abstract The Stone theorem requires that in a physical Hilbert space $${{{\mathcal {H}}}}$$ H the time-evolution of a stable quantum system is unitary if and only if the corresponding Hamiltonian H is self-adjoint. Sometimes, a simpler picture of the evolution may be constructed in a manifestly unphysical Hilbert space $${{{\mathcal {K}}}}$$ K in which H is nonhermitian but $${{\mathcal {PT}}}$$ PT -symmetric. In applications, unfortunately, one only rarely succeeds in circumventing the key technical obstacle which lies in the necessary reconstruction of the physical Hilbert space $${{{\mathcal {H}}}}$$ H . For a $${{\mathcal {PT}}}$$ PT -symmetric version of the spiked harmonic oscillator we show that in the dynamical regime of the unavoided level crossings such a reconstruction of $${{{\mathcal {H}}}}$$ H becomes feasible and, moreover, obtainable by non-numerical means. The general form of such a reconstruction of $${{{\mathcal {H}}}}$$ H enables one to render every exceptional unavoided-crossing point tractable as a genuine, phenomenologically most appealing quantum-phase-transition instant.

scholarly journals SCALING OF VON NEUMANN ENTROPY AT THE ANDERSON TRANSITION

2010 ◽  
Vol 24 (12n13) ◽  
pp. 1823-1840 ◽  
Author(s):  
Sudip Chakravarty
Keyword(s):  
Phase Transition ◽  
Wave Function ◽  
Phase Transitions ◽  
Ground State ◽  
Quantum Phase Transitions ◽  
Quantum Phase ◽  
Tuning Parameter ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Anderson Transition

Extensive body of work has shown that for the model of a non-interacting electron in a random potential there is a quantum critical point for dimensions greater than two — a metal–insulator transition. This model also plays an important role in the plateau-to-plateu transition in the integer quantum Hall effect, which is also correctly captured by a scaling theory. Yet, in neither of these cases the ground state energy shows any non-analyticity as a function of a suitable tuning parameter, typically considered to be a hallmark of a quantum phase transition, similar to the non-analyticity of the free energy in a classical phase transition. Here we show that von Neumann entropy (entanglement entropy) is non-analytic at these phase transitions and can track the fundamental changes in the internal correlations of the ground state wave function. In particular, it summarizes the spatially wildly fluctuating intensities of the wave function close to the criticality of the Anderson transition. It is likely that all quantum phase transitions can be similarly described.

scholarly journals Superconductor–insulator transition in capacitively coupled superconducting nanowires

2020 ◽  
Vol 11 ◽  
pp. 1402-1408
Author(s):  
Alex Latyshev ◽  
Andrew G Semenov ◽  
Andrei D Zaikin
Keyword(s):  
Phase Transition ◽  
Quantum Phase Transitions ◽  
Quantum Phase ◽  
Superconducting Nanowires ◽  
Capacitively Coupled ◽  
Renormalization Group Equations ◽  
Mutual Capacitance ◽  
Quantum Phase Slips ◽  
Insulator Phase Transition ◽  
Phase Slips

We investigate superconductor–insulator quantum phase transitions in ultrathin capacitively coupled superconducting nanowires with proliferating quantum phase slips. We derive a set of coupled Berezinskii–Kosterlitz–Thouless-like renormalization group equations demonstrating that interaction between quantum phase slips in one of the wires gets modified due to the effect of plasma modes propagating in another wire. As a result, the superconductor–insulator phase transition in each of the wires is controlled not only by its own parameters but also by those of the neighboring wire as well as by mutual capacitance. We argue that superconducting nanowires with properly chosen parameters may turn insulating once they are brought sufficiently close to each other.

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 Multiple quantum phase transitions of different nature in the topological kagome magnet Co3Sn2−xInxS2

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Z. Guguchia ◽  
H. Zhou ◽  
C. N. Wang ◽  
J.-X. Yin ◽  
C. Mielke ◽  
...  
Keyword(s):  
Phase Transition ◽  
Quantum Phase Transitions ◽  
Muon Spin ◽  
Quantum Critical Point ◽  
Quantum Phase ◽  
Muon Spin Rotation ◽  
Multiple Quantum ◽  
Zero Temperature ◽  
In Doping ◽  
Out Of Plane

AbstractThe exploration of topological electronic phases that result from strong electronic correlations is a frontier in condensed matter physics. One class of systems that is currently emerging as a platform for such studies are so-called kagome magnets based on transition metals. Using muon spin-rotation, we explore magnetic correlations in the kagome magnet Co3Sn2−xInxS2 as a function of In-doping, providing putative evidence for an intriguing incommensurate helimagnetic (HM) state. Our results show that, while the undoped sample exhibits an out-of-plane ferromagnetic (FM) ground state, at 5% of In-doping the system enters a state in which FM and in-plane antiferromagnetic (AFM) phases coexist. At higher doping, a HM state emerges and becomes dominant at the critical doping level of only xcr,1 ≃ 0.3. This indicates a zero temperature first order quantum phase transition from the FM, through a mixed state, to a helical phase at xcr,1. In addition, at xcr,2 ≃ 1, a zero temperature second order phase transition from helical to paramagnetic phase is observed, evidencing a HM quantum critical point (QCP) in the phase diagram of the topological magnet Co3Sn2−xInxS2. The observed diversity of interactions in the magnetic kagome lattice drives non-monotonous variations of the topological Hall response of this system.

scholarly journals Observation of generalized Kibble-Zurek mechanism across a first-order quantum phase transition in a spinor condensate

2020 ◽  
Vol 6 (21) ◽  
pp. eaba7292
Author(s):  
L.-Y. Qiu ◽  
H.-Y. Liang ◽  
Y.-B. Yang ◽  
H.-X. Yang ◽  
T. Tian ◽  
...  
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Power Law ◽  
Quantum Phase Transition ◽  
Scaling Laws ◽  
Quantum Phase Transitions ◽  
Quantum Phase ◽  
Polar Phase ◽  
First Order ◽  
Spin Excitations

The Kibble-Zurek mechanism provides a unified theory to describe the universal scaling laws in the dynamics when a system is driven through a second-order quantum phase transition. However, for first-order quantum phase transitions, the Kibble-Zurek mechanism is usually not applicable. Here, we experimentally demonstrate and theoretically analyze a power-law scaling in the dynamics of a spin-1 condensate across a first-order quantum phase transition when a system is slowly driven from a polar phase to an antiferromagnetic phase. We show that this power-law scaling can be described by a generalized Kibble-Zurek mechanism. Furthermore, by experimentally measuring the spin population, we show the power-law scaling of the temporal onset of spin excitations with respect to the quench rate, which agrees well with our numerical simulation results. Our results open the door for further exploring the generalized Kibble-Zurek mechanism to understand the dynamics across first-order quantum phase transitions.

scholarly journals Observation of a quantum phase transition in the quantum Rabi model with a single trapped ion

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
M.-L. Cai ◽  
Z.-D. Liu ◽  
W.-D. Zhao ◽  
Y.-K. Wu ◽  
Q.-X. Mei ◽  
...  
Keyword(s):  
Phase Transition ◽  
Thermodynamic Limit ◽  
Quantum Phase Transitions ◽  
Paul Trap ◽  
Single Mode ◽  
Quantum Phase ◽  
Controlled Study ◽  
Many Body ◽  
Rabi Model ◽  
Many Body Systems

AbstractQuantum phase transitions (QPTs) are usually associated with many-body systems in the thermodynamic limit when their ground states show abrupt changes at zero temperature with variation of a parameter in the Hamiltonian. Recently it has been realized that a QPT can also occur in a system composed of only a two-level atom and a single-mode bosonic field, described by the quantum Rabi model (QRM). Here we report an experimental demonstration of a QPT in the QRM using a 171Yb+ ion in a Paul trap. We measure the spin-up state population and the average phonon number of the ion as two order parameters and observe clear evidence of the phase transition via adiabatic tuning of the coupling between the ion and its spatial motion. An experimental probe of the phase transition in a fundamental quantum optics model without imposing the thermodynamic limit opens up a window for controlled study of QPTs and quantum critical phenomena.

scholarly journals Quantum phase transitions of strongly correlated metals

2020 ◽  
pp. 6-13
Author(s):  
Martha Yolima Suárez Villagrán ◽  
Nikolaos Mitsakos ◽  
John H. Miller Jr
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Critical Temperature ◽  
Quantum Phase Transition ◽  
Open Problem ◽  
Quantum Phase Transitions ◽  
Quantum Phase ◽  
Strongly Correlated ◽  
Made In

In this article, we discuss several aspects of the quantum phase transition, with special emphasis on the metalinsulator transition. We start with a review of key experimental and theoretical works and then discuss how doping a system reduces the critical temperature of the overall phase transition. Although many aspects of the quantum phase transition still remain an open problem, onsiderable progress has been made in revealing the underlying physics, both theoretically and experimentally.

scholarly journals Spherical model and quantum phase transitions

2021 ◽  
Vol 2094 (2) ◽  
pp. 022027
Author(s):  
V N Udodov
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Critical Temperature ◽  
Critical Exponents ◽  
Quantum Phase Transitions ◽  
Dimensional Space ◽  
Spherical Model ◽  
Quantum Phase ◽  
Two Dimensional ◽  
Epsilon Expansion

Abstract The spherical Berlin-Katz model is considered in the framework of the epsilon expansion in one-dimensional and two-dimensional space. For the two-dimensional and threedimensional cases in this model, an exact solution was previously obtained in the presence of a field, and for the two-dimensional case the critical temperature is zero, that is, a “quantum” phase transition is observed. On the other hand, the epsilon expansion of critical exponents with an arbitrary number of order parameter components is known. This approach is consistent with the scaling paradigm. Some critical exponents are found for the spherical model in one-and twodimensional space in accordance with the generalized scaling paradigm and the ideas of quantum phase transitions. A new formula is proposed for the critical heat capacity exponent, which depends on the dynamic index z, at a critical temperature equal to zero. An expression is proposed for the order of phase transition with a change in temperature (developing the approach of R. Baxter), which also depends on the z index. An interpolation formula is presented for the effective dimension of space, which is valid for both a positive critical temperature and a critical temperature equal to zero. This formula is general. Transitions with a change in the field in a spherical model at absolute zero are also considered.

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