Numerical variational simulations of quantum phase transitions in the sub-Ohmic spin-boson model with multiple polaron ansatz

With extensive variational simulations, dissipative quantum phase transitions in the sub-Ohmic spin-boson model are numerically studied in a dense limit of environmental modes. By employing a generalized trial wave function composed of coherent-state expansions, transition points and critical exponents are accurately determined for various spectral exponents, demonstrating excellent agreement with those obtained by other sophisticated numerical techniques. Besides, the quantum-to-classical correspondence is fully confirmed over the entire sub-Ohmic range, compared with theoretical predictions of the long-range Ising model. Mean-field and non-mean-field critical behaviors are found in the deep and shallow sub-Ohmic regimes, respectively, and distinct physical mechanisms of them are uncovered.Comment: 10 pages, 9 figures, 2 table

Transient dynamics of a one-dimensional Holstein polaron under the influence of an external electric field

Following the Dirac-Frenkel time-dependent variational principle, transient dynamics of a one-dimensional Holstein polaron with diagonal and off-diagonal exciton-phonon coupling in an external electric field is studied by employing the multi-D$_2$ {\it Ansatz}, also known as a superposition of the usual Davydov D$_2$ trial states. Resultant polaron dynamics has significantly enhanced accuracy, and is in perfect agreement with that derived from the hierarchy equations of motion method. Starting from an initial broad wave packet, the exciton undergoes typical Bloch oscillations. Adding weak exciton-phonon coupling leads to a broadened exciton wave packet and a reduced current amplitude. Using a narrow wave packet as the initial state, the bare exciton oscillates in a symmetric breathing mode, but the symmetry is easily broken by weak coupling to phonons, resulting in a non-zero exciton current. For both scenarios, temporal periodicity is unchanged by exciton-phonon coupling. In particular, at variance with the case of an infinite linear chain, no steady state is found in a finite-sized ring within the anti-adiabatic regime. For strong diagonal coupling, the multi-$\rm D_2$ {\it Anstaz} is found to be highly accurate, and the phonon confinement gives rise to exciton localization and decay of the Bloch oscillations

Polaron dynamics with a multitude of Davydov D2_2 trial states

We propose an extension to the Davydov D$_2$ Ansatz in the dynamics study of the Holstein molecular crystal model with diagonal and off-diagonal exciton-phonon coupling using the Dirac-Frenkel time-dependent variational principle. The new trial state by the name of the "multi-D$_2$ Ansatz" is a linear combination of Davydov D$_2$ trial states, and its validity is carefully examined by quantifying how faithfully it follows the Schr\"odinger equation. Considerable improvements in accuracy have been demonstrated in comparison with the usual Davydov trial states, i.e., the single D$_1$ and D$_2$ Ans\"atze. With an increase in the number of the Davydov D$_2$ trial states in the multi-D$_2$ Ansatz, deviation from the exact Schr\"odinger dynamics is gradually diminished, leading to a numerically exact solution to the Schr\"odinger equation.Comment: 14 pages, 15 figure

Ground state properties of sub-Ohmic spin-boson model with simultaneous diagonal and off-diagonal coupling

By employing the variational approach, density matrix renormalization group (DMRG), exact diagonalization as well as symmetry and mean-field analyses, the ground state properties of the two-bath spin boson model with simultaneous diagonal and off-diagonal coupling are systematically studied in the sub-Ohmic regime. A novel quantum phase transition from a doubly degenerate "localized phase" to the other doubly degenerate "delocalized phase" is uncovered. Via the multi-D1 ansatz as the variational wave function, transition points are determined accurately, consistent with the results from DMRG and exact diagonalization. An effective spatial dimension $d_{eff} = 2.37(6)$ is then estimated, which is found to be compatible with the mean-field prediction. Furthermore, the quantum phase transition is inferred to be of first order for the baths described by a continuous spectral density function. In the case of single mode, however, the transition is softened.Comment: revised version after the paper is publishe

Inverse Symmetry in Complete Genomes and Whole-Genome Inverse Duplication

The cause of symmetry is usually subtle, and its study often leads to a deeper understanding of the bearer of the symmetry. To gain insight into the dynamics driving the growth and evolution of genomes, we conducted a comprehensive study of textual symmetries in 786 complete chromosomes. We focused on symmetry based on our belief that, in spite of their extreme diversity, genomes must share common dynamical principles and mechanisms that drive their growth and evolution, and that the most robust footprints of such dynamics are symmetry related. We found that while complement and reverse symmetries are essentially absent in genomic sequences, inverse–complement plus reverse–symmetry is prevalent in complex patterns in most chromosomes, a vast majority of which have near maximum global inverse symmetry. We also discovered relations that can quantitatively account for the long observed but unexplained phenomenon of -mer skews in genomes. Our results suggest segmental and whole-genome inverse duplications are important mechanisms in genome growth and evolution, probably because they are efficient means by which the genome can exploit its double-stranded structure to enrich its code-inventory

Competition between diagonal and off-diagonal coupling gives rise to charge-transfer states in polymeric solar cells

It has long been a puzzle on what drives charge separation in artificial polymeric solar cells as a consensus has yet to emerge among rivaling theories based upon electronic localization and delocalization pictures. Here we propose an alternative using the two-bath spin-boson model with simultaneous diagonal and off-diagonal coupling: the critical phase, which is born out of the competition of the two coupling types, and is neither localized nor delocalized. The decoherence-free feature of the critical phase also helps explain sustained coherence of the charge-transfer state. Exploiting Hamiltonian symmetries in an enhanced algorithm of density-matrix renormalization group, we map out boundaries of the critical phase to a precision previously unattainable, and determine the bath spectral densities inducive to the existence of the charge-transfer state.Published versio

Variational dynamics of the sub-Ohmic spin-boson model on the basis of multiple Davydov D1 states

Dynamics of the sub-Ohmic spin-boson model is investigated by employing a multitude of the Davydov D1 trial states, also known as the multi-D1Ansatz. Accuracy in dynamics simulations is improved significantly over the single D1Ansatz, especially in the weak system-bath coupling regime. The reliability of the multi-D1Ansatz for various coupling strengths and initial conditions is also systematically examined, with results compared closely with those of the hierarchy equations of motion and the path integral Monte Carlo approaches. In addition, a coherent-incoherent phase crossover in the nonequilibrium dynamics is studied through the multi-D1Ansatz. The phase diagram is obtained with a critical pointsc = 0.4. For sc < s < 1, the coherent-to-incoherent crossover occurs at a certain coupling strength, while the coherent state recurs at a much larger coupling strength. For s < sc, only the coherent phase exists.Published versio