Ryan V. Mishmash

Quantum entangled dark solitons formed by ultracold atoms in optical lattices.

Inspired by experiments on Bose-Einstein condensates in optical lattices, we study the quantum evolution of dark soliton initial conditions in the context of the Bose-Hubbard Hamiltonian. An extensive set of quantum measures is utilized in our analysis, including von Neumann and generalized quantum entropies, quantum depletion, and the pair correlation function. We find that quantum effects cause the soliton to fill in. Moreover, soliton-soliton collisions become inelastic, in strong contrast to the predictions of mean-field theory. These features show that the lifetime and collision properties of dark solitons in optical lattices provide clear signals of quantum effects.

Ising anyons in frustration-free Majorana-dimer models

Dimer models have long been a fruitful playground for understanding topological physics. Here, we introduce a class, termed Majorana-dimer models, wherein bosonic dimers are decorated with pairs of Majorana modes. We find that the simplest examples of such systems realize an intriguing, intrinsically fermionic phase of matter that can be viewed as the product of a chiral Ising theory, which hosts deconfined non-Abelian quasiparticles, and a topological p_x−ip_y superconductor. While the bulk anyons are described by a single copy of the Ising theory, the edge remains fully gapped. Consequently, this phase can arise in exactly solvable, frustration-free models. We describe two parent Hamiltonians: one generalizes the well-known dimer model on the triangular lattice, while the other is most naturally understood as a model of decorated fluctuating loops on a honeycomb lattice. Using modular transformations, we show that the ground-state manifold of the latter model unambiguously exhibits all properties of the Ising×(p_x−ip_y) theory. We also discuss generalizations with more than one Majorana mode per site, which realize phases related to Kitaevs 16-fold way in a similar fashion.

Non-Fermi-liquid d -wave metal phase of strongly interacting electrons

Developing a theoretical framework for conducting electronic fluids qualitatively distinct from those described by Landau’s Fermi-liquid theory is of central importance to many outstanding problems in condensed matter physics. One such problem is that, above the transition temperature and near optimal doping, high-transition-temperature copper-oxide superconductors exhibit ‘strange metal’ behaviour that is inconsistent with being a traditional Landau Fermi liquid. Indeed, a microscopic theory of a strange-metal quantum phase could shed new light on the interesting low-temperature behaviour in the pseudogap regime and on the d-wave superconductor itself. Here we present a theory for a specific example of a strange metal—the ‘d-wave metal’. Using variational wavefunctions, gauge theoretic arguments, and ultimately large-scale density matrix renormalization group calculations, we show that this remarkable quantum phase is the ground state of a reasonable microscopic Hamiltonian—the usual t–J model with electron kinetic energy t and two-spin exchange J supplemented with a frustrated electron ‘ring-exchange’ term, which we here examine extensively on the square lattice two-leg ladder. These findings constitute an explicit theoretical example of a genuine non-Fermi-liquid metal existing as the ground state of a realistic model.

Theory of a Competitive Spin Liquid State for Weak Mott Insulators on the Triangular Lattice

We propose a novel quantum spin liquid state that can explain many of the intriguing experimental properties of the low-temperature phase of the organic spin liquid candidate materials κ-(BEDT-TTF)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2. This state of paired fermionic spinons preserves all symmetries of the system, and it has a gapless excitation spectrum with quadratic bands that touch at momentum k[over →]=0. This quadratic band touching is protected by symmetries. Using variational Monte Carlo techniques, we show that this state has highly competitive energy in the triangular lattice Heisenberg model supplemented with a realistically large ring-exchange term.

Approaching a topological phase transition in Majorana nanowires

Recent experiments have produced mounting evidence of Majorana zero modes in nanowire-superconductor hybrids. Signatures of an expected topological phase transition accompanying the onset of these modes nevertheless remain elusive. We investigate a fundamental question concerning this issue: Do well-formed Majorana modes necessarily entail a sharp phase transition in these setups? Assuming reasonable parameters, we argue that finite-size effects can dramatically smooth this putative transition into a crossover, even in systems large enough to support well-localized Majorana modes. We propose overcoming such finite-size effects by examining the behavior of low-lying excited states through tunneling spectroscopy. In particular, the excited-state energies exhibit characteristic field and density dependence, and scaling with system size, that expose an approaching topological phase transition. We suggest several experiments for extracting the predicted behavior. As a useful byproduct, the protocols also allow one to measure the wires spin-orbit coupling directly in its superconducting environment.

Exotic Gapless Mott Insulators of Bosons on Multileg Ladders

We present evidence for an exotic gapless insulating phase of hard-core bosons on multileg ladders with a density commensurate with the number of legs. In particular, we study in detail a model of bosons moving with direct hopping and frustrating ring exchange on a 3-leg ladder at ν=1/3 filling. For sufficiently large ring exchange, the system is insulating along the ladder but has two gapless modes and power law transverse density correlations at incommensurate wave vectors. We propose a determinantal wave function for this phase and find excellent comparison between variational Monte Carlo and density matrix renormalization group calculations on the model Hamiltonian, thus providing strong evidence for the existence of this exotic phase. Finally, we discuss extensions of our results to other N-leg systems and to N-layer two-dimensional structures.

Bose metals and insulators on multileg ladders with ring exchange

We establish compelling evidence for the existence of new quasi-one-dimensional descendants of the d-wave Bose liquid (DBL), an exotic two-dimensional quantum phase of uncondensed itinerant bosons characterized by surfaces of gapless excitations in momentum space [O. I. Motrunich and M. P. A. Fisher Phys. Rev. B 75 235116 (2007)]. In particular, motivated by a strong-coupling analysis of the gauge theory for the DBL, we study a model of hard-core bosons moving on the N-leg square ladder with frustrating four-site ring exchange. Here, we focus on four- and three-leg systems where we have identified two novel phases: a compressible gapless Bose metal on the four-leg ladder and an incompressible gapless Mott insulator on the three-leg ladder. The former is conducting along the ladder and has five gapless modes, one more than the number of legs. This represents a significant step forward in establishing the potential stability of the DBL in two dimensions. The latter, on the other hand, is a fundamentally quasi-one-dimensional phase that is insulating along the ladder but has two gapless modes and incommensurate power-law transverse density-density correlations. While we have already presented results on this latter phase elsewhere [ M. S. Block et al. Phys. Rev. Lett. 106 046402 (2011)], we will expand upon those results in this work. In both cases, we can understand the nature of the phase using slave-particle-inspired variational wave functions consisting of a product of two distinct Slater determinants, the properties of which compare impressively well to a density matrix renormalization group solution of the model Hamiltonian. Stability arguments are made in favor of both quantum phases by accessing the universal low-energy physics with a bosonization analysis of the appropriate quasi-1D gauge theory. We will briefly discuss the potential relevance of these findings to high-temperature superconductors, cold atomic gases, and frustrated quantum magnets.

Reply to Comment on "Quantum Entangled Dark Solitons formed by Ultracold Atoms in Optical Lattices"

In our entangled many-body quantum simulations we obtained three lines of evidence that mean-field-like dark solitons decay when taken as an initial condition: fillingin of the pair correlation function g; inelasticity of soliton-soliton collisions; and comparison of the exact quantum depletion of the macroscopic mode associated with the mean-field versus what one obtains with a weakly interacting Bogoliubov description. The latter is covered in a great deal more detail in [1]. Dziarmaga et al. have showed that filling-in of g does not necessarily correspond to filling-in or decay of a soliton in a single quantum measurement; that is, the soliton may delocalize, so that it fills in on average, but retain its soliton-like character in any single experiment, in keeping with well-established previous studies [2]. Martin and Ruostekoski have verified this result with an independent method [3, 4]. Dziarmaga et al.’s simulation of a single-shot measurement treats the near-mean-field regime in which the filling factor for each site is 5000/31 ≃ 161. They also work with an assumed mean-field soliton profile of a tanh function centered at different positions to build the delocalized soliton state. Our work uses a filling factor of 1/2 to 2, and is not in the mean-field regime (although in the ground-state phase diagram our choices of hopping, interaction, and filling do correspond to the superfluid region, not the Mott-insulating one). We agree with Dziarmaga et al. that filling in of g does not necessarily correspond to soliton decay in a single measurement. However, the common difficulty of connecting results of near-mean-field simulations to entangled quantum manybody simulations remains; large filling factors have a different phenomenology than small filling factors, and one cannot use simulations from one regime to make a statement about simulations in the other. Dziarmaga et al.’s results are in a different regime from ours, and moreover have not dealt with our other two pieces of evidence for dark soliton decay. In a separate work [5–7], one of us has studied the quantum analog of dark solitons over all interaction regimes, from a mean field Bose-Einstein condensate to a Tonks-Girardeau gas. We showed that it is in fact yrast states that properly play the role of phase slip, not in general mean-field-like dark solitons. These yrast states are precisely Lieb’s type-II excitations, which were identified with dark solitons in the weakly-interacting limit only. It is an intriguing open question as to whether or not anything like a dark soliton exists in the medium to strongly interacting regime, i.e., a well-defined, robust density notch which collides elastically with other solitons. In either case, the mean-field dark soliton is very far from the quantum dark soliton, as we have shown in [7], and thus we believe that mean-field dark solitons, e.g., Dziarmaga et al.’s superposition of tanh condensates, decay when injected into the quantum theory out of the near-mean-field regime (we note that the initial conditions in our Letter are close to symmetry-broken versions of Dziarmaga et al.’s tanh function). The specific parameters for which mean-field theory breaks down for this problem were obtained via the Bethe ansatz, and the connection to the delocalization concept is discussed in more detail in [8]. We thank Iacopo Carusotto, Rina Kanamoto, Carlos Lobo, Andrew D. Martin, Janne Ruostekoski, Alice Sinatra, and Masahito Ueda for useful discussions. We acknowledge support from the National Science Foundation under Grant PHY-0547845 as part of the NSF CAREER program.