Bound-state dynamics in one-dimensional multispecies fermionic systems

Azaria, P.

doi:10.1103/physrevb.95.125106

Cited by 3 publications

(5 citation statements)

References 59 publications

(133 reference statements)

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“…We also find that the low energy fix point has a higher symmetry with respect to interaction between modes that the original model, signalling a dynamically emergent symmetry. This phenomenon was previously observed in the context of three leg ladders [61][62][63][64][65][66][67][68][69][70][71][72]. In our case, the massive phases are ground states of a Hamiltonian that is obtained by marginal deformations of an emergent SU(3) symmetry, which is not present in the UV, but that manifest itself in the IR.…”

Section: Discussion and Outlooksupporting

confidence: 77%

Interplay between intrinsic and emergent topological protection on interacting helical modes

2019

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The interplay between topology and interactions on the edge of a two dimensional topological insulator with time reversal symmetry is studied. We consider a simple non-interacting system of three helical channels with an inherent Z2 topological protection, and hence a zero-temperature conductance of G = e 2 /h. We show that when interactions are added to the model, the ground state exhibits two different phases as function of the interaction parameters. One of these phases is a trivial insulator at zero temperature, as the symmetry protecting the non-interacting topological phase is spontaneously broken. In this phase there is zero conductance (G = 0) at zerotemperature. The other phase displays enhanced topological properties, with a topologically protected zero-temperature conductance of G = 3e 2 /h and an emergent Z3 symmetry not present in the lattice model. The neutral sector in this phase is described by a massive version of Z3 parafermions. This state is an example of a dynamically enhanced symmetry protected topological state.

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Section: Discussion and Outlooksupporting

confidence: 77%

Interplay between intrinsic and emergent topological protection on interacting helical modes

2019

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“…This is characterized by the formation of bound states of N fermions (analogous to baryons in high-energy physics) and the suppression of Cooper pairs. A related phase has already been stabilized in other one-dimensional systems [312][313][314][315][316]. b. BCS singlet pairing phase.…”

Section: Molecular Luttinger Liquids and Zn Quantum Criticalitymentioning

confidence: 94%

Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods

et al. 2018

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We review two important non-perturbative approaches for extracting the physics of low- dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of confor- mal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symme- tries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1+1D quantum chro- modynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. We describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.

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“…The charge-1 fermion (22) can hence be interpreted as a spinless fermion with an enlarged Fermi surface at ±N k F . Furthermore, as discussed in [25], the system may be viewed as a fermionic Luttinger liquid made of interacting composite fermionic particles with Luttinger parameter K. In this respect notice that when N = 1, the composite fermionic particle is identical to the bare fermion, and one recovers the usual Luttinger liquid description.…”

Section: N Odd and Composite Fermionic Excitationsmentioning

confidence: 99%

“…As before, we assume that in the low-energy limit the phases associated with different flavors are locked together. Denoting the collective phase by Θ(x, τ ) the effective low-energy Lagrangian of the system is that of a generalized Luttinger liquid [25]…”

Section: Low-energy Description Of the Topological Phasementioning

confidence: 99%

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From one-dimensional charge conserving superconductors to the gapless Haldane phase

2018

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We develop a framework to analyze one-dimensional topological superconductors with charge conservation. In particular, we consider models with N flavors of fermions and (Z2) N symmetry, associated with the conservation of the fermionic parity of each flavor. For a single flavor, we recover the result that a distinct topological phase with exponentially localized zero modes does not exist due to absence of a gap to single particles in the bulk. For N > 1, however, we show that the ends of the system can host low-energy, exponentially-localized modes. The analysis can readily be generalized to systems in other symmetry classes. To illustrate these ideas, we focus on lattice models with SO (N ) symmetric interactions, and study the phase transition between the trivial and the topological gapless phases using bosonization and a weak-coupling renormalization group analysis. As a concrete example, we study in detail the case of N = 3. We show that in this case, the topologically non-trivial superconducting phase corresponds to a gapless analogue of the Haldane phase in spin-1 chains. In this phase, although the bulk is gapless to single particle excitations, the ends host spin-1/2 degrees of freedom which are exponentially localized and protected by the spin gap in the bulk. We obtain the full phase diagram of the model numerically, using density matrix renormalization group calculations. Within this model, we identify the self-dual line studied by Andrei and Destri [Nucl. Phys. B, 231(3), 445-480 (1984)], as a first-order transition line between the gapless Haldane phase and a trivial gapless phase. This allows us to identify the propagating spin-1/2 kinks in the Andrei-Destri model as the topological end-modes present at the domain walls between the two phases.

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Bound-state dynamics in one-dimensional multispecies fermionic systems

Cited by 3 publications

References 59 publications

Interplay between intrinsic and emergent topological protection on interacting helical modes

Interplay between intrinsic and emergent topological protection on interacting helical modes

Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods

From one-dimensional charge conserving superconductors to the gapless Haldane phase

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