Soumya Bera

Many-body localization characterized from a one-particle perspective

We show that the one-particle density matrix ρ can be used to characterize the interaction-driven many-body localization transition in closed fermionic systems. The natural orbitals (the eigenstates of ρ) are localized in the many-body localized phase and spread out when one enters the delocalized phase, while the occupation spectrum (the set of eigenvalues of ρ) reveals the distinctive Fock-space structure of the many-body eigenstates, exhibiting a steplike discontinuity in the localized phase. The associated one-particle occupation entropy is small in the localized phase and large in the delocalized phase, with diverging fluctuations at the transition. We analyze the inverse participation ratio of the natural orbitals and find that it is independent of system size in the localized phase.

Generalized multipolaron expansion for the spin-boson model: Environmental entanglement and the biased two-state system

We develop a systematic variational coherent-state expansion for themany-body ground state of the spin-boson model, in which a quantum two-level system is coupled to a continuum of harmonic oscillators. Energetic constraints at the heart of this technique are rationalized in terms of polarons (displacements of the bath states in agreement with classical expectations) and antipolarons (counterdisplacements due to quantum tunneling effects). We present a comprehensive study of the ground-state two-level system population and coherence as a function of tunneling amplitude, dissipation strength, and bias (akin to asymmetry of the double-well potential defining the two-state system). The entanglement among the different environmental modes is investigated by looking at spectroscopic signatures of the bipartite entanglement entropy between a given environmental mode and all the other modes. We observe a drastic change in behavior of this entropy for increasing dissipation, indicative of the entangled nature of the environmental states. In addition, the entropy spreads over a large energy range at strong dissipation, a testimony to the wide entanglement window characterizing the underlying Kondo state. Finally, comparisons to accurate numerical renormalization-group calculations and to the exact Bethe ansatz solution of the model demonstrate the rapid convergence of our variationally optimized multipolaron expansion, suggesting that it should also be a useful tool for dissipative models of greater complexity, as relevant for numerous systems of interest in quantum physics and chemistry.

Stabilizing Spin Coherence Through Environmental Entanglement in Strongly Dissipative Quantum Systems

The key feature of a quantum spin coupled to a harmonic bath-a model dissipative quantum system-is competition between oscillator potential energy and spin tunneling rate. We show that these opposing tendencies cause environmental entanglement through superpositions of adiabatic and antiadiabatic oscillator states, which then stabilizes the spin coherence against strong dissipation. This insight motivates a fast-converging variational coherent-state expansion for the many-body ground state of the spin-boson model, which we substantiate via numerical quantum tomography.

Quantum Mutual Information as a Probe for Many-Body Localization

We demonstrate that the quantum mutual information (QMI) is a useful probe to study many-body localization (MBL). First, we focus on the detection of a metal-insulator transition for two different models, the noninteracting Aubry-André-Harper model and the spinless fermionic disordered Hubbard chain. We find that the QMI in the localized phase decays exponentially with the distance between the regions traced out, allowing us to define a correlation length, which converges to the localization length in the case of one particle. Second, we show how the QMI can be used as a dynamical indicator to distinguish an Anderson insulator phase from a MBL phase. By studying the spread of the QMI after a global quench from a random product state, we show that the QMI does not spread in the Anderson insulator phase but grows logarithmically in time in the MBL phase.

Dirty Weyl semimetals: Stability, phase transition, and quantum criticality

We study the stability of three-dimensional incompressible Weyl semimetals in the presence of random quenched charge impurities. Combining numerical analysis and scaling theory we show that in the presence of sufficiently weak randomness (i) Weyl semimetal remains stable, while (ii) double-Weyl semimetal gives rise to compressible diffusive metal where the mean density of states at zero energy is finite. At stronger disorder, Weyl semimetal undergoes a quantum phase transition and enter into a metallic phase. Mean density of states at zero energy serves as the order parameter and displays single-parameter scaling across such disorder driven quantum phase transition. We numerically determine various exponents at the critical point, which appear to be insensitive to the number of Weyl pairs. We also extract the extent of the quantum critical regime in disordered Weyl semimetal and the phase diagram of dirty double Weyl semimetal at finite energies.

One-particle density matrix characterization of many-body localization

We study interacting fermions in one dimension subject to random, uncorrelated onsite disorder, a paradigmatic model of many-body localization (MBL). This model realizes an interaction-driven quantum phase transition between an ergodic and a many-body localized phase, with the transition occurring in the many-body eigenstates. We propose a single-particle framework to characterize these phases by the eigenstates (the natural orbitals) and the eigenvalues (the occupation spectrum) of the one-particle density matrix (OPDM) in individual many-body eigenstates. As a main result, we find that the natural orbitals are localized in the MBL phase, but delocalized in the ergodic phase. This qualitative change in these single-particle states is a many-body effect, since without interactions the single-particle energy eigenstates are all localized. The occupation spectrum in the ergodic phase is thermal in agreement with the eigenstate thermalization hypothesis, while in the MBL phase the occupations preserve a discontinuity at an emergent Fermi edge. This suggests that the MBL eigenstates are weakly dressed Slater determinants, with the eigenstates of the underlying Anderson problem as reference states. We discuss the statistical properties of the natural orbitals and of the occupation spectrum in the two phases and as the transition is approached. Our results are consistent with the existing picture of emergent integrability and localized integrals of motion, or quasiparticles, in the MBL phase. We emphasize the close analogy of the MBL phase to a zero-temperature Fermi liquid: in the studied model, the MBL phase is adiabatically connected to the Anderson insulator and the occupation-spectrum discontinuity directly indicates the presence of quasiparticles localized in real space. Finally, we show that the same picture emerges for interacting fermions in the presence of an experimentally-relevant bichromatic lattice and thereby demonstrate that our findings are not limited to a specific model.

Quantum size effects in the atomistic structure of armchair nanoribbons

(Dated: November 16, 2011)Quantum size effects in armchair graphene nano-ribbons (AGNR) with hydrogen termination areinvestigated via density functional theory (DFT) in Kohn-Sham formulation. “Selection rules” willbe formulated, that allow to extract (approximately) the electronic structure of the AGNR bandsstarting from the four graphene dispersion sheets. In analogy with the case of carbon nanotubes, athreefold periodicity of the excitation gap with the ribbon width (N, number of carbon atoms percarbon slice) is predicted that is confirmed by ab initio results. While traditionally such a periodicitywould be observed in electronic response experiments, the DFT analysis presented here shows thatit can also be seen in the ribbon geometry: the length of a ribbon with L slices approaches thelimiting value for a very large width 1 ≪ N (keeping the aspect ratio small N ≪ L) with 1/N-oscillations that display the electronic selection rules. The oscillation amplitude is so strong, thatthe asymptotic behavior is non-monotonous, i.e., wider ribbons exhibit a stronger elongation thanmore narrow ones.

Anatomy of quantum critical wave functions in dissipative impurity problems

Quantum phase transitions reflect singular changes taking place in a many-body ground state;however, computing and analyzing large-scale critical wave functions constitutes a formidable challenge. Physical insights into the sub-Ohmic spin-boson model are provided by the coherent-state expansion (CSE), which represents the wave function by a linear combination of classically displaced configurations. We find that the distribution of low-energy displacements displays an emergent symmetry in the absence of spontaneous symmetry breaking while experiencing strong fluctuations of the order parameter near the quantum critical point. Quantum criticality provides two strong fingerprints in critical low-energy modes: an algebraic decay of the average displacement and a constant universal average squeezing amplitude. These observations, confirmed by extensive variational matrix-product-state (VMPS) simulations and field theory arguments, offer precious clues into the microscopics of critical many-body states in quantum impurity models.

Spontaneous emission of Schrödinger cats in a waveguide at ultrastrong coupling

Josephson circuits provide a realistic physical setup where the light–matter fine structure constant can become of order one, allowing to reach a regime dominated by non-perturbative effects beyond standard quantum optics. Simple processes, such as spontaneous emission, thus acquire a many-body character, that can be tackled using a new description of the time-dependent state vector in terms of quantum-superposed coherent states. We find that spontaneous atomic decay at ultrastrong coupling leads to the emission of spectrally broad Schrodinger cats rather than of monochromatic single photons. These cats states remain partially entangled with the emitter at intermediate stages of the dynamics, even after emission, due to a large separation in time scales between fast energy relaxation and exponentially slow decoherence. Once decoherence of the qubit is finally established, quantum information is completely transfered to the state of the emitted cat.

Local entanglement structure across a many-body localization transition

Local entanglement between pairs of spins, as measured by concurrence, is investigated in a disordered spin model that displays a transition from an ergodic to a many-body localized phase in excited states. It is shown that the concurrence vanishes in the ergodic phase and becomes nonzero and increases in the many-body localized phase. This happen to be correlated with the transition in the spectral statistics from Wigner to Poissonian distribution. A scaling form is found to exist in the second derivative of the concurrence with the disorder strength. It also displays a critical value for the localization transition that is close to what is known in the literature from other measures. An exponential decay of concurrence with distance between spins is observed in the localized phase. Nearest neighbor spin concurrence in this phase is also found to be strongly correlated with the disorder configuration of onsite fields: nearly similar fields implying larger entanglement.