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Register a new userFluctuating local field approach to free energy of 1D molecules with strong collective electronic correlations
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The impact of leading collective electronic fluctuations on a free energy of a prototype 1D model for molecular systems is considered within the recently developed Fluctuating Local Field (FLF) approach. The FLF method is a non-perturbative extension of a mean-field theory, where a self-consistent effective constant field is replaced by a fluctuating one. Integrating the fluctuating field out numerically exactly allows to account for collective electronic fluctuations mediated by this field without any assumptions on their magnitude, degree of nonlinearity, etc. Using a half-filled Hubbard ring as a benchmark system, we find that the FLF method noticeably improves a mean-field estimation for the free energy, in particular below the mean-field Neel temperature. We further demonstrate that the mean-field result can be even more improved introducing a multi-mode FLF scheme that additionally takes into account sub-leading fluctuations. Possible applications for the thermodynamics of real molecules are also discussed.
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We review recent results on the properties of materials with correlated electrons obtained within the LDA+DMFT approach, a combination of a conventional band structure approach based on the local density approximation (LDA) and the dynamical mean-field theory (DMFT). The application to four outstanding problems in this field is discussed: (i) we compute the full valence band structure of the charge-transfer insulator NiO by explicitly including the p-d hybridization, (ii) we explain the origin for the simultaneously occuring metal-insulator transition and collapse of the magnetic moment in MnO and Fe2O3, (iii) we describe a novel GGA+DMFT scheme in terms of plane-wave pseudopotentials which allows us to compute the orbital order and cooperative Jahn-Teller distortion in KCuF3 and LaMnO3, and (iv) we provide a general explanation for the appearance of kinks in the effective dispersion of correlated electrons in systems with a pronounced three-peak spectral function without having to resort to the coupling of electrons to bosonic excitations. These results provide a considerable progress in the fully microscopic investigations of correlated electron materials.
We establish a way to handle main collective fluctuations in correlated quantum systems based on a Fluctuation Local Field concept. This technique goes beyond standard mean-field approaches, such as Hartree-Fock and dynamical mean-field theories (DMFT), as it includes a fluctuating classical field that acts on the leading order parameter of the system. Effective model parameters of this new theory are determined from the variational principle, which allows to resolve the Fierz ambiguity in decoupling of the local interaction term. In the saddle-point approximation for the fluctuating field our method reproduces the mean-field result. The exact numerical integration over this field allows to consider nonlinear fluctuations of the global order parameter of the system while local correlations can be accounted by solving the DMFT impurity problem. We apply our method to the magnetic susceptibility of finite Hubbard systems at half-filling and demonstrate that the introduced technique leads to a superior improvement of results with respect to parental mean-field approaches without significant numerical complications. We show that the Fluctuation Local Field method can be used in a very broad range of temperatures substantially below the Neel temperature of DMFT, which remains a major challenge for all existing theoretical approaches.
In one dimension, the area law and its implications for the approximability by Matrix Product States are the key to efficient numerical simulations involving quantum states. Similarly, in simulations involving quantum operators, the approximability by Matrix Product Operators (in Hilbert-Schmidt norm) is tied to an operator area law, namely the fact that the Operator Space Entanglement Entropy (OSEE)---the natural analog of entanglement entropy for operators, investigated by Zanardi [Phys. Rev. A 63, 040304(R) (2001)] and by Prosen and Pizorn [Phys. Rev. A 76, 032316 (2007)]---, is bounded. In the present paper, it is shown that the OSEE can be calculated in two-dimensional conformal field theory, in a number of situations that are relevant to questions of simulability of long-time dynamics in one spatial dimension. It is argued that: (i) thermal density matrices $rho propto e^{-beta H}$ and Generalized Gibbs Ensemble density matrices $rho propto e^{- H_{rm GGE}}$ with local $H_{rm GGE}$ generically obey the operator area law; (ii) after a global quench, the OSEE first grows linearly with time, then decreases back to its thermal or GGE saturation value, implying that, while the operator area law is satisfied both in the initial state and in the asymptotic stationary state at large time, it is strongly violated in the transient regime; (iii) the OSEE of the evolution operator $U(t) = e^{-i H t}$ increases linearly with $t$, unless the Hamiltonian is in a localized phase; (iv) local operators in Heisenberg picture, $phi(t) = e^{i H t} phi e^{-i H t}$, have an OSEE that grows sublinearly in time (perhaps logarithmically), however it is unclear whether this effect can be captured in a traditional CFT framework, as the free fermion case hints at an unexpected breakdown of conformal invariance.
Strong electronic correlations related to a repulsive local interaction suppress the electronic compressibility in a single-band model, and the capacitance of a corresponding metallic film is directly related to its electronic compressibility. Both statements may be altered significantly when two extensions to the system are implemented which we investigate here: (i) we introduce an attractive nearest-neighbor interaction $V$ as antagonist to the repulsive on-site repulsion $U$, and (ii) we consider nano-structured multilayers (heterostructures) assembled from two-dimensional layers of these systems. We determine the respective total compressibility $kappa$ and capacitance $C$ of the heterostructures within a strong coupling evaluation, which builds on a Kotliar-Ruckenstein slave-boson technique. Whereas the capacitance $C(n)$ for electronic densities $n$ close to half-filling is suppressed---illustrated by a correlation induced dip in $C(n)$---it may be appreciably enhanced close to a van Hove singularity. Moreover, we show that the capacitance may be a non-monotonic function of $U$ close to half-filling for both attractive and repulsive $V$. The compressibility $kappa$ can differ from $C$ substantially, as $kappa$ is very sensitive to internal electrostatic energies which in turn depend on the specific set-up of the heterostructure. In particular, we show that a capacitor with a polar dielectric has a smaller electronic compressibility and is more stable against phase separation than a standard non-polar capacitor with the same capacitance.
We develop a truncated Hamiltonian method to study nonequilibrium real time dynamics in the Schwinger model - the quantum electrodynamics in D=1+1. This is a purely continuum method that captures reliably the invariance under local and global gauge transformations and does not require a discretisation of space-time. We use it to study a phenomenon that is expected not to be tractable using lattice methods: we show that the 1+1D quantum electrodynamics admits the dynamical horizon violation effect which was recently discovered in the case of the sine-Gordon model. Following a quench of the model, oscillatory long-range correlations develop, manifestly violating the horizon bound. We find that the oscillation frequencies of the out-of-horizon correlations correspond to twice the masses of the mesons of the model suggesting that the effect is mediated through correlated meson pairs. We also report on the cluster violation in the massive version of the model, previously known in the massless Schwinger model. The results presented here reveal a novel nonequilibrium phenomenon in 1+1D quantum electrodynamics and make a first step towards establishing that the horizon violation effect is present in gauge field theory.
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