arXiv subjects

Balázs Hetényi

Publications and source records attributed to Balázs Hetényi.

26 records · Page 2Linked to original sources

arXiv2016

Current, conduction, and localization in quantum many-body systems

A representation of current is presented which can account for ideal conduction and distinguish superconductors, superfluids, ideal, and non-ideal conductors. The idea of the scheme is that different current operators and transport weights can be constructed based on the number of charge carriers in basic units of conduction. Ideal conductors with basic units of $p$ charge carriers exhibit a flux quantization rule of $Φ_B=nhc/(pe)$ (for example $p=2$ for BCS). Extension of the current operators to lattice systems is also presented. A full diagonalization calculation for an interacting model of spinless fermions of all the transport coefficients is carried out. It is shown that in a number of strongly correlated models ideal conduction involving the simultaneous motion of all charge carriers is possible.

cond-mat.supr-con↗

arXiv2015

Quantum quench in 2D using the variational Baeriswyl wavefunction

By combining the Baeriswyl wavefunction with equilibrium and time-dependent variational principles, we develop a non-equilibrium formalism to study quantum quenches for two dimensional spinless fermions with nearest-neighbour hopping and repulsion. The variational ground state energy and the short time dynamics agree convincingly with the results of numerically exact simulations. We find that depending on the initial and final interaction strength, the quenched system either exhibits undamped oscillations or relaxes to a time independent steady state. The time averaged expectation value of the CDW order parameter rises sharply when crossing from the steady state regime to the oscillating regime, indicating that the system, being non-integrable, shows signs of thermalization with an effective temperature above or below the equilibrium critical temperature, respectively.

cond-mat.str-el↗

arXiv2015

Impurity coupled to an artificial magnetic field in a Fermi gas in a ring trap

The dynamics of a single impurity interacting with a many particle background is one of the central problems of condensed matter physics. Recent progress in ultracold atom experiments makes it possible to control this dynamics by coupling an artificial gauge field specifically to the impurity. In this paper, we consider a narrow toroidal trap in which a Fermi gas is interacting with a single atom. We show that an external magnetic field coupled to the impurity is a versatile tool to probe the impurity dynamics. Using Bethe Ansatz (BA) we calculate the eigenstates and corresponding energies exactly as a function of the flux through the trap. Adiabatic change of flux connects the ground state to excited states due to flux quantization. For repulsive interactions, the impurity disturbs the Fermi sea by dragging the fermions whose momentum matches the flux. This drag transfers momentum from the impurity to the background and increases the effective mass. The effective mass saturates to the total mass of the system for infinitely repulsive interactions. For attractive interactions, the drag again increases the effective mass which quickly saturates to twice the mass of a single particle as a polaron of the impurity and one fermion is formed. For excited states with momentum comparable to number of particles, effective mass shows a resonant behavior. We argue that standard tools in cold atom experiments can be used to test these predictions.

cond-mat.quant-gas↗

arXiv2014

Drude weight, Meissner weight, rotational inertia of bosonic superfluids: how are they distinguished?

The Drude weight, the quantity which distinguishes metals from insulators, is proportional to the second derivative of the ground state energy with respect to a flux at zero flux. The same expression also appears in the definition of the Meissner weight, the quantity which indicates superconductivity, as well as in the definition of non-classical rotational inertia of bosonic superfluids. It is shown that the difference between these quantities depends on the interpretation of the average momentum term, which can be understood as the expectation value of the total momentum (Drude weight), the sum of the expectation values of single momenta (rotational inertia of a superfluid), or the sum over expectation values of momentum pairs (Meissner weight). This distinction appears naturally when the current from which the particular transport quantity is derived is cast in terms of shift operators.

cond-mat.str-el↗

arXiv2014

Cumulants associated with geometric phases

The Berry phase can be obtained by taking the continuous limit of a cyclic product $-\mbox{Im} \ln \prod_{I=0}^{M-1} \langle Ψ_0({\boldsymbol ξ}_I)|Ψ_0({\boldsymbol ξ}_{I+1})\rangle$, resulting in the circuit integral $i \oint \mbox{d}{\boldsymbol ξ} \cdot \langle Ψ_0({\boldsymbol ξ})|\nabla_{\boldsymbol ξ}|Ψ_0({\boldsymbol ξ}\rangle$. Considering a parametrized curve ${\boldsymbol ξ}(χ)$ we show that the product $\prod_{I=0}^{M-1} \langle Ψ_0(χ_I)|Ψ_0( χ_{I+1})\rangle$ can be equated to a cumulant expansion. The first contributing term of this expansion is the Berry phase itself, the other terms are the associated spread, skew, kurtosis, etc. The cumulants are shown to be gauge invariant. It is also shown that these quantities can be expressed in terms of an operator.

math-ph↗

arXiv2013

dc conductivity as a geometric phase

The zero frequency conductivity ($D_c$), the criterion to distinguish between conductors and insulators is expressed in terms of a geometric phase. $D_c$ is also expressed using the formalism of the modern theory of polarization. The tenet of Kohn [{\it Phys. Rev.} {\bf 133} A171 (1964)], namely, that insulation is due to localization in the many-body space, is refined as follows. Wavefunctions which are eigenfunctions of the total current operator give rise to a finite $D_c$ and are therefore metallic. They are also delocalized. Several examples which corroborate the results are presented, as well as a numerical implementation. The formalism is also applied to the Hall conductance, and the quantization condition for zero Hall conductance is derived to be $\frac{eΦ_B}{N h c} = \frac{Q}{M}$, with $Q$ and $M$ integers.

cond-mat.other↗

arXiv2012

Current Response in Extended Systems as a Geometric Phase: Application to Variational Wavefunctions

The linear response theory for current is investigated in a variational context. Expressions are derived for the Drude and superfluid weights for general variational wavefunctions. The expression for the Drude weight highlights the difficulty in its calculation since it depends on the exact energy eigenvalues which are usually not available in practice. While the Drude weight is not available in a simple form, the linear current response is shown to be expressible in terms of a geometric phase, or alternatively in terms of the expectation value of the total position shift operator. The contribution of the geometric phase to the current response is then analyzed for some commonly used projected variational wavefunctions (Baeriswyl, Gutzwiller, and combined). It is demonstrated that this contribution is independent of the projectors themselves and is determined by the wavefunctions onto which the projectors are applied.

cond-mat.str-el↗

arXiv2012

Drude and Superfluid Weights in Extended Systems: the Role of Discontinuities and $δ$-peaks in the One and Two-Body Momentum Densities

The question of conductivity is revisited. Using the total momentum shift operator to construct the perturbed many-body Hamiltonian and ground state wave function the second derivative of the ground state energy with respect to the perturbing field is expressed in terms of the one and two-body momentum densities. The distinction between the adiabatic and envelope function derivatives, hence that between the Drude and superfluid weights can be introduced in a straightforward manner. It is shown that a discontinuity in the momentum density leads to a contribution to the Drude weight, but not the superfluid weight, however a $δ$-function contribution in the two-body momentum density (such as in the BCS wave-funtion) contributes to both quantities. The connection between the discontinuity in the momentum density and localization is also demonstrated.

cond-mat.str-el↗