arXiv subjects

Mats Granath

Publications and source records attributed to Mats Granath.

32 records · Page 2Linked to original sources

arXiv2019

Quantum error correction for the toric code using deep reinforcement learning

We implement a quantum error correction algorithm for bit-flip errors on the topological toric code using deep reinforcement learning. An action-value Q-function encodes the discounted value of moving a defect to a neighboring site on the square grid (the action) depending on the full set of defects on the torus (the syndrome or state). The Q-function is represented by a deep convolutional neural network. Using the translational invariance on the torus allows for viewing each defect from a central perspective which significantly simplifies the state space representation independently of the number of defect pairs. The training is done using experience replay, where data from the algorithm being played out is stored and used for mini-batch upgrade of the Q-network. We find performance which is close to, and for small error rates asymptotically equivalent to, that achieved by the Minimum Weight Perfect Matching algorithm for code distances up to $d=7$. Our results show that it is possible for a self-trained agent without supervision or support algorithms to find a decoding scheme that performs on par with hand-made algorithms, opening up for future machine engineered decoders for more general error models and error correcting codes.

quant-ph↗

arXiv2018

Suppression of superfluid stiffness near Lifshitz-point instability to finite momentum superconductivity

We derive the effective Ginzburg-Landau theory for finite momentum (FFLO/PDW) superconductivity without spin population imbalance from a model with local attraction and repulsive pair-hopping. We find that the GL free energy must include up to sixth order derivatives of the order parameter, providing a unified description of the interdependency of zero and finite momentum superconductivity. For weak pair-hopping the phase diagram contains a line of Lifshitz points where vanishing superfluid stiffness induces a continuous change to a long wavelength Fulde-Ferrell (FF) state. For larger pair-hopping there is a bicritical region where the pair-momentum changes discontinuously. Here the FF type state is near degenerate with the Larkin-Ovchinnikov (LO) or Pair-Density-wave (PDW) type state. At the intersection of these two regimes there is a "Super-Lifshitz" point with extra soft fluctuations. The instability to finite momentum superconductivity occurs for arbitrarily weak pair-hopping for sufficiently large attraction suggesting that even a small repulsive pair-hopping may be significant in a microscopic model of strongly correlated superconductivity. Several generic features of the model may have bearing on the cuprate superconductors, including the suppression of superfluid stiffness in proximity to a Lifshitz point as well as the existence of subleading FFLO order (or vice versa) in the bicritical regime.

cond-mat.supr-con↗

arXiv2017

Effective model for a supercurrent in a pair-density wave

We extend the standard effective model of d-wave superconductivity of a single band tight-binding Hamiltonian with nearest-neighbor attraction to include finite range periodically modulated pair-hopping. The pair-hopping is characterized by a fixed wave number $\pmb{\mathcal{Q}}=\mathcal{Q}\hat{x}$ breaking lattice rotational symmetry. Within self-consistent BCS theory we study the general variational state consisting of two incommensurate singlet pair amplitudes $Δ_{{\bf Q}_1}$ and $Δ_{{\bf Q}_2}$ and find two types of near degenerate ground states; of the Larkin-Ovchnnikov (LO) or pair-density wave (PDW) type with $Δ_{{\bf Q}_1}=Δ_{{\bf Q}_2}$ and ${\bf Q}_1=-{\bf Q}_2\approx \mathcal{Q}$ or of the Fulde-Ferrell (FF) type with $Δ_{{\bf Q}_2}=0$ and ${\bf Q}_1\approx \pm \mathcal{Q}$. An anomalous term in the static current operator arising from the pair-hopping ensures that Bloch's theorem on zero current in the ground state is enforced also for the FF ground state, despite broken time-reversal symmetry without spin-population imbalance. We also consider a supercurrent by exploring the space of pair-momenta ${\bf Q}_1$ and ${\bf Q}_2$ and identify characteristics of a state with multiple finite momentum order-parameters. This includes the possibility of phase-separation of current densities and spontaneous mirror-symmetry breaking manifested in the directional dependence of the depairing current.

cond-mat.str-el↗

arXiv2016

Diffusion and localization of relative strategy scores in the Minority Game

We study the equilibrium distribution of relative strategy scores of agents in the asymmetric phase ($α\equiv P/N\gtrsim 1$) of the basic Minority Game using sign-payoff, with $N$ agents holding two strategies over $P$ histories. We formulate a statistical model that makes use of the gauge freedom with respect to the ordering of an agent's strategies to quantify the correlation between the attendance and the distribution of strategies. The relative score $x\in\mathbb{Z}$ of the two strategies of an agent is described in terms of a one dimensional random walk with asymmetric jump probabilities, leading either to a static and asymmetric exponential distribution centered at $x=0$ for fickle agents or to diffusion with a positive or negative drift for frozen agents. In terms of scaled coordinates $x/\sqrt{N}$ and $t/N$ the distributions are uniquely given by $α$ and in quantitative agreement with direct simulations of the game. As the model avoids the reformulation in terms of a constrained minimization problem it can be used for arbitrary payoff functions with little calculational effort and provides a transparent and simple formulation of the dynamics of the basic Minority Game in the asymmetric phase.

cond-mat.dis-nn↗

arXiv2014

Signatures of coherent electronic quasiparticles in the paramagnetic Mott insulator

We show that the Mott insulating state of the half-filled paramagnetic Hubbard model in infinite dimensions contains electronic quasiparticles with very small quasiparticle weight at the inner edge of the Hubbard bands. We use a stochastic and non-perturbative quantum impurity solver based on calculating the impurity self energy as a sample average over a representative distribution of impurity models solved by exact diagonalization. Due to the natural parallelization of the method, millions of poles are readily generated for the self energy which allows to work with very small pole-broadening $η$. Solutions at small and large $η$ are qualitatively different, and only at $η\leq 0.001$ (in units of half bare band width) are quasiparticles found. Evaluated on the imaginary frequency axis we find that the small $η$ solutions agree within statistical error with results using continuous time quantum Monte Carlo.

cond-mat.str-el↗

arXiv2013

Bilayer graphene spectral function in RPA and self-consistent GW

We calculate the single-particle spectral function for doped bilayer graphene in the low energy limit, described by two parabolic bands with zero band gap and long range Coulomb interaction. Calculations are done using thermal Green's functions in both the random phase approximation (RPA) and the fully self-consistent GW approximation. RPA (in line with previous studies) yields a spectral function which apart from the Landau quasiparticle peaks shows additional coherent features interpreted as plasmarons, i.e. composite electron-plasmon excitations. In GW the plasmaron becomes incoherent and peaks are replaced by much broader features. The deviation of the quasiparticle weight and mass renormalization from their non-interacting values is small which indicates that bilayer graphene is a weakly interacting system. The electron energy loss function, $Im[-ε^{-1}_q(ω)]$ shows a sharp plasmon mode in RPA which in GW approximation becomes less coherent and thus consistent with the weaker plasmaron features in the corresponding single-particle spectral function.

cond-mat.mes-hall↗

arXiv2012

Distributional exact diagonalization formalism for quantum impurity models

We develop a method for calculating the self-energy of a quantum impurity coupled to a continuous bath by stochastically generating a distribution of finite Anderson models that are solved by exact diagonalization, using the noninteracting local spectral function as a probability distribution for the sampling. The method enables calculation of the full analytic self-energy and single-particle Green's function in the complex frequency plane, without analytic continuation, and can be used for both finite and zero temperature at arbitrary fillings. Results are in good agreement with imaginary frequency data from continuous-time quantum Monte Carlo calculations for the single impurity Anderson model and the two-orbital Hubbard model within dynamical mean field theory (DMFT) as well as real frequency data for self energy of the single band Hubbard model within DMFT using numerical renormalization group. The method should be applicable to a wide range of quantum impurity models and particularly useful when high-precision real frequency results are sought.

cond-mat.str-el↗

arXiv2011

Lattice expansion from isotope substitution in the Iron based superconductors

We estimate the changes in lattice parameters due to iron isotope substitution in the iron-based high temperature superconductors using a variational calculation based on the anharmonicity of the Fe-As(Se) bond. For BaFe2As2 and 57Fe to 54$Fe substitution we find a c-axis expansion of 1 10^{-3}Å and in-plane a-axis contraction of 1 10^{-5}Å at 250K in good agreement with experimental values on (Ba,K)Fe2As2 for which a negative isotope exponent α=-\frac{d\ln T_c}{d\ln m}<0 was found [P.M. Shirage et al., Phys. Rev. Lett. 103, 257003 (2009)]. For FeSe in contrast we find an expansion for both a and c lattice parameters. We discuss the relevance of these isotope induced changes of lattice parameters to the isotope effect in light of the well established sensitivity to the Fe-As(Se) coordination.

cond-mat.supr-con↗

arXiv2011

Discretized Thermal Green's Functions

We present a spectral weight conserving formalism for Fermionic thermal Green's functions that are discretized in imaginary time and thus periodic in imaginary ("Matsubara") frequency. The formalism requires a generalization of the Dyson equation and the Baym-Kadanoff-Luttinger-Ward functional for the free energy. A conformal transformation is used to analytically continue the periodized Matsubara Green's function to the continuous real axis in a way that conserves the discontinuity at t=0 of the corresponding real-time Green's function. For given discretization the method allows numerical Green's function calculations of very high precision and it appears to give a well controlled convergent approximation as we decrease the discretization interval. The ideas are tested on Dynamical Mean Field Theory calculations of the paramagnetic Hubbard model.

cond-mat.str-el↗

arXiv2010

The Dynamical Mean Field Theory phase space extension and critical properties of the finite temperature Mott transition

We consider the finite temperature metal-insulator transition in the half filled paramagnetic Hubbard model on the infinite dimensional Bethe lattice. A new method for calculating the Dynamical Mean Field Theory fixpoint surface in the phase diagram is presented and shown to be free from the convergence problems of standard forward recursion. The fixpoint equation is then analyzed using dynamical systems methods. On the fixpoint surface the eigenspectra of its Jacobian is used to characterize the hysteresis boundaries of the first order transition line and its second order critical end point. The critical point is shown to be a cusp catastrophe in the parameter space, opening a pitchfork bifurcation along the first order transition line, while the hysteresis boundaries are shown to be saddle-node bifurcations of two merging fixpoints. Using Landau theory the properties of the critical end point is determined and related to the critical eigenmode of the Jacobian. Our findings provide new insights into basic properties of this intensively studied transition.

cond-mat.str-el↗

arXiv2006

Nodal-antinodal dichotomy and magic doping fractions in a stripe ordered antiferromagnet

We study a model of a stripe ordered doped antiferromagnet consisting of coupled Hubbard ladders which can be tuned from quasi-one-dimensional to two-dimensional. We solve for the magnetization and charge density on the ladders by Hartree-Fock theory and find a set of solutions with lightly doped ``spin-stripes'' which are antiferromagnetic and more heavily doped anti-phase ``charge-stripes''. Both the spin- and charge-stripes have electronic spectral weight near the Fermi energy but in different regions of the Brillouin zone; the spin-stripes in the ``nodal'' region, near (π/2,π/2), and the charge-stripes in the ``antinodal'' region, near (π,0). We find a striking dichotomy between nodal and antinodal states in which the nodal states are essentially delocalized and two-dimensional whereas the antinodal states are quasi-one-dimensional, localized on individual charge-stripes. For bond-centered stripes we also find an even-odd effect of the charge periodicity which could explain the non-monotonous variations with doping of the low-temperature resistivity in LSCO

cond-mat.str-el↗

arXiv2006

Exact Transformation for Spin-Charge Separation of Spin-half Fermions without Constraints

We demonstrate an exact local transformation which maps a purely Fermionic manybody system to a system of spinfull Bosons and spinless Fermions, demonstrating a possible path to a non-Fermi liquid state. We apply this to the half-filled Hubbard model and show how the transformation maps the ordinary spin half Fermionic degrees of freedom exactly and without introducing Hilbert space constraints to a charge-like ``quasicharge'' fermion and a spin-like ``quasispin'' Boson while preserving all the symmetries of the model. We present approximate solutions with localized charge which emerge naturally from the Hubbard model in this form. Our results strongly suggest that charge tends to remain localized for large values of the Hubbard U.

cond-mat.str-el↗

arXiv2004

Band structure of Charge Ordered Doped Antiferromagnets

We study the distribution of electronic spectral weight in a doped antiferromagnet with various types of charge order and compare to angle resolved photoemission experiments on lightly doped La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) and electron doped Nd$_{2-x}$Ce$_x$CuO$_{4\pmδ}$. Calculations on in-phase stripe and bubble phases for the electron doped system are both in good agreement with experiment including in particular the existence of in-gap spectral weight. In addition we find that for in-phase stripes, in contrast to anti-phase stripes, the chemical potential is likely to move with doping. For the hole doped system we find that ``staircase'' stripes which are globally diagonal but locally vertical or horizontal can reproduce the photoemission data whereas pure diagonal stripes cannot. We also calculate the magnetic structure factors of such staircase stripes and find that as the stripe separation is decreased with increased doping these evolve from diagonal to vertical separated by a coexistence region. The results suggest that the transition from horizontal to diagonal stripes seen in neutron scattering on underdoped LSCO may be a crossover between a regime where the typical length of straight stripe segments is longer than the inter-stripe spacing to one where it is shorter and that locally the stripes are always aligned with the Cu-O bonds.

cond-mat.supr-con↗

arXiv1999

One-Dimensional Electron Liquid in an Antiferromagnetic Environment: Spin Gap from Magnetic Correlations

We study a one-dimensional electron liquid coupled by a weak spin-exchange interaction to an antiferromagnetic spin-S ladder with n legs. A perturbative renormalization group analysis in the semiclassical limit reveals the opening of a spin gap, driven by the local magnetic correlations on the ladder. The effect, which we argue is present for any gapful ladder or gapless ladder with $nS\gg 1$, is enhanced by the repulsive interaction among the conduction electrons but is insensitive to the sign of the spin exchange interaction with the ladder. Possible implications for the striped phases of the cuprates are discussed.

cond-mat.str-el↗