Quantum Phase Transitions In Systems Research Articles

Environmentally induced effects and dynamical phase transitions in quantumsystems

The dynamics of open quantum systems is determined by singularities in thecontinuum of scattering wavefunctions which are related to avoided and true crossingsof eigenvalue trajectories of a non-Hermitian Hamiltonian. The phases of theeigenfunctions are not rigid in approaching the crossing points so that environmentallyinduced spectroscopic redistribution processes may take place and a dynamicalphase transition may occur. Due to the formal equivalence between the quantummechanical Schrödinger equation and the optical wave equation in symmetric lattices, the dynamics of the system is determined also in this latter case byavoided and true crossings of eigenvalue trajectories of the non-Hermitian Hamiltonian. Incontrast to the eigenvalues characterizing an open quantum system, the eigenvaluesdescribing the symmetric optical lattice are real as long as the influence of the environment (lattice) onthe optical wave equation is small. In the regime of avoided level crossings, the symmetry isbroken, the eigenvalues become complex and a dynamical phase transition occurs, similaras in the open quantum system. These results can be proven experimentally by tracingthe phase rigidity of the eigenfunctions of the Hamiltonian and its correlationwith the transparency. The redistribution processes in the regime of avoided levelcrossings allow us to design systems with desired properties in a broad parameterrange.

Dynamical Phase Transitions in Quantum Systems

Many years ago Bohr characterized the fundamental differences between the two extreme cases of quantum mechanical many-body problems known at that time: between the compound states in nuclei at extremely high level density and the shell-model states in atoms at low level density. It is shown in the present paper that the compound nucleus states at high level density are the result of a dynamical phase transition due to which they have lost any spectroscopic relation to the individual states of the nucleus. The last ones are shell-model states which are of the same type as the shell-model states in atoms. Mathematically, dynamical phase transitions are caused by singular (exceptional) points at which the trajectories of the eigenvalues of the non-Hermitian Hamilton operator cross. In the neighborhood of these singular points, the phases of the eigenfunctions are not rigid. It is possible therefore that some eigenfunctions of the system align to the scattering wavefunctions of the environment by decoupling (trapping) the remaining ones from the environment. In the Schrodinger equation, nonlinear terms appear in the neighborhood of the singular points.

Monte Carlo approach to phase transitions in quantum systems

We propose algorithms of the path-ingetral-based quantum Monte Carlo simulation, which is otherwise prohibitively slow. While the basic idea is the loop-cluster update, there are some important ‘tricks’ that are vital to make the simulation practical. In the present paper, we show two such techniques and their successful applications to the two-dimensional SU(N) Heisenberg model and the three-dimensional Bose Hubbard model. In the former, we obtain a new type of the valence-bond-solid state for the two-boson representation, while in the latter we equillibrate a system of which the size is comparable to a typical experiment of optical lattices.

Quantum phase transitions in systems of parallel quantum dots

We study the low-temperature transport properties of systems of parallel quantum dots described by the $N$-impurity Anderson model. We calculate the quasiparticle scattering phase shifts, spectral functions, and correlations as a function of the gate voltage for $N$ up to 5. For any $N$, the conductance at the particle-hole symmetric point is unitary. For $N\ensuremath{\ge}2$, a transition from ferromagnetic to antiferromagnetic impurity spin correlations occurs at some gate voltage. For $N\ensuremath{\ge}3$, there is an additional transition due to an abrupt change in average impurity occupancy. For odd $N$, the conductance is discontinuous through both quantum phase transitions, while for even $N$ only the magnetic transition affects the conductance. Similar effects should be experimentally observable in systems of quantum dots with ferromagnetic conduction-band-mediated interdot exchange interactions.

Entanglement in fermionic systems at a quantum phase transition

We consider recent results on the use of the single-site entanglement measure for identifying and characterizing a quantum phase transition in systems of interacting fermions. We discuss the extension of these results to fermionic models where the single-site entanglement may fail to signal a quantum phase transition, with particular attention given to the one-dimensional extended UV Hubbard model.

Thermodynamic analogy for quantum phase transitions at zero temperature

We propose a relationship between thermodynamic phase transitions and ground-state quantum phase transitions in systems with variable Hamiltonian parameters. It is based on a link between zeros of the canonical partition function at complex temperatures and exceptional points of a quantum Hamiltonian in the complex-extended parameter space. This approach is applied in the interacting boson model, where it is shown to properly distinguish the first- and second-order phase transitions.

Disorder-induced rounding of certain quantum phase transitions.

We study the influence of quenched disorder on quantum phase transitions in systems with overdamped dynamics. For Ising order-parameter symmetry disorder destroys the sharp phase transition by rounding because a static order parameter can develop on rare spatial regions. This leads to an exponential dependence of the order parameter on the coupling constant. At finite temperatures the static order on the rare regions is destroyed. This restores the phase transition and leads to a double-exponential relation between critical temperature and coupling strength. We discuss the behavior based on Lifshitz-tail arguments and illustrate the results by simulations of a model system.

Exotic quantum phase transition in systems with quenched disorder

Exotic quantum phase transition in systems with quenched disorder

Quantum phase transitions in electronic systems

AbstractQuantum phase transitions occur at zero temperature when some non‐thermal control‐parameter like pressure or chemical composition is changed. They are driven by quantum rather than thermal fluctuations. In this review we first give a pedagogical introduction to quantum phase transitions and quantum critical behavior emphasizing similarities with and differences to classical thermal phase transitions. We then illustrate the general concepts by discussing a few examples of quantum phase transitions occurring in electronic systems. The ferromagnetic transition of itinerant electrons shows a very rich behavior since the magnetization couples to additional electronic soft modes which generates an effective long‐range interaction between the spin fluctuations. We then consider the influence of rare regions on quantum phase transitions in systems with quenched disorder, taking the antiferromagnetic transitions of itinerant electrons as a primary example. Finally we discuss some aspects of the metal‐insulator transition in the presence of quenched disorder and interactions.

A microscopic approach to phase transitions in quantum systems

We present a new theoretical approach for the study of the phase diagram of interacting quantum particles: bosons, fermions or spins. In the neighborhood of a phase transition, the expected renormalization group structure is recovered both near the upper and lower critical dimension. Information on the microscopic Hamiltonian is also retained and no mapping to effective field theories is needed. A simple approximation to our formally exact equations is studied for the spin-S Heisenberg model in three dimensions where explicit results for critical exponents, critical temperature and coexistence curve are obtained.

Solution of the spectral problem for the Schrödinger equation with a degenerate polynomial potential of even power

We study the stationary Schrodinger equation with the degenerate potential U(x) = x2r, r e Z+, which describes phase transitions in quantum systems. The symmetry of the problem is revealed and an analytical procedure is developed for finding the eigenvalues of such potentials. The eigenvalues and the lowest energy levels are found numerically for r=2, 3, ..., 18.

Zero-temperature phase transitions in quantum systems with symmetry-conserving impurities

Abstract The zero-temperature phase transitions in several quantum systems with quenched symmetry-conserving impurities are investigated on the grounds of a diagrammatic approach, starting from an appropriate random quantum field functional Hamiltonian. We find that the peculiar random anisotropy induced along the imaginary-time axis by the competition between random and quantum regime fluctuations inhibits the occurence of a sharp second-order transition, in agreement with the renormalization group predictions. In particular, for three-dimensional Ising-like systems a spin-glass-like behavior appears, while for systems with continuous symmetry only smeared or first-order transitions seem to be possible. An explicit calculation in the large- n limit suggests that the second alternative is more realistic. Additional insight is obtained by reformulating the problem by means of Bogolubov's variational principle. Its intrinsic simplicity gives the possibility to obtain informations for dimensionalities d > 1 and offers the occasion for some methodological remarks. Finally, in the light of our results, we put forward a possible interpretation of recent experiments on some mixed crystals.

Flux equilibria in quantum systems far away from thermal equilibrium

Quasi-probability functions make it possible to study flux equilibria and phase transitions in quantum systems far from thermal equilibrium using concepts of classical statistical mechanics.