Related papers: Geometric Critical Exponents in Classical and Quan…
In rotations with a binary symbolic dynamics, a critical curve is the locus of parameters for which the boundaries of the partition that defines the symbolic dynamics are connected via a prescribed number of iterations and symbolic…
Quantum criticality describes the collective fluctuations of matter undergoing a second-order phase transition at zero temperature. It is being discussed in a number of strongly correlated electron systems. A prototype case occurs in the…
Path integral formulation of quantum mechanics defines the wavefunction associated with a particle as a sum of phase-factors, which are periodic functions of classical action. In the present article, this periodicity is shown to impart the…
A series of geometric concepts are formulated for $\mathcal{PT}$-symmetric quantum mechanics and they are further unified into one entity, i.e., an extended quantum geometric tensor (QGT). The imaginary part of the extended QGT gives a…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
Critical transitions, or large changes in the state of a system after a small change in the system's external conditions or parameters, commonly occur in a wide variety of disciplines, from the biological and social sciences to physics.…
Scaling ideas and renormalization group approaches proved crucial for a deep understanding and classification of critical phenomena in thermal equilibrium. Over the past decades, these powerful conceptual and mathematical tools were…
We study a random matrix model for the statistical properties of the purity of a bipartite quantum system at a finite (fictitious) temperature. This enables us to write the generating function for the cumulants, for both balanced and…
It is well known that phase transitions arise if the interaction among particles embodies an attractive as well as a repulsive contribution. In this work it will be shown that the breakdown of Lorentz symmetry, characterized through a…
Matrix product states, a key ingredient of numerical algorithms widely employed in the simulation of quantum spin chains, provide an intriguing tool for quantum phase transition engineering. At critical values of the control parameters on…
The critical phenomena associated to the liquid to solid transition of quasi-two-dimensional vibrated granular systems is studied using molecular dynamics simulations of the inelastic hard sphere model. The critical properties are…
We construct a class of quantum critical points with non-mean-field critical exponents via holography. Our approach is phenomenological. Beginning with the D3/D5 system at nonzero density and magnetic field which has a chiral phase…
The geometry of the classical phase space C of a finite number of degrees of freedom determines the possible duality symmetries of the corresponding quantum mechanics. Under duality we understand the relativity of the notion of a quantum…
The geometry of quantum states can be an indicator of criticality, yet it remains less explored under non-Hermitian topological conditions. In this work, we unveil diverse scalings of the quantum geometry over the ground state manifold…
The geometric phase induced in an auxiliary qubit by a many-body system is calculated and discussed. Two kinds of coupling between the auxiliary qubit and the many-body system are considered, which lead to dephasing and dissipation in the…
We investigate the geometry of a critical system undergoing a second order thermal phase transition. Using a local description for the dynamics characterizing the system at the critical point T=Tc, we reveal the formation of clusters with…
Critical phenomena in globally coupled excitable elements are studied by focusing on a saddle-node bifurcation at the collective level. Critical exponents that characterize divergent fluctuations of interspike intervals near the bifurcation…
Using an exact solution of the one-dimensional (1D) quantum transverse-field Ising model (TFIM), we calculate the critical exponents of the two-dimensional (2D) anisotropic classical Ising model (IM). We verify that the exponents are the…
Starting with the generally well accepted opinion that quantizing an arbitrary Hamiltonian system involves picking out some additional structure on the classical phase space (the {\sl shadow} of quantum mechanics in the classical theory),…
We describe two dimensional models with a metallic Fermi surface which display quantum phase transitions controlled by strongly interacting critical field theories below their upper critical dimension. The primary examples involve…