Emergent mode and bound states in single-component one-dimensional lattice fermionic systems

Abstract

We study the formation of bound states in a one-dimensional, single-component Fermi chain with attractive interactions. The phase diagram, computed from DMRG (density matrix renormalization group), shows not only a superfluid of paired fermions (pair phase) and a liquid of fermion triplets (trion phase), but also a phase with two gapless modes. We show that the latter phase is described by a 2-component Tomonaga-Luttinger liquid (TLL) theory, consisting of one charged and one neutral mode. We argue based on our numerical data, that the single, pair, and trion phases are descendants of the 2-component TLL theory. We speculate on the nature of the phase transitions amongst these phases.Tomonaga-Luttinger liquid (TLL) theory captures the physics of many 1-D quantum systems like spin chains, spin ladders, nanotubes [1], nanowires [2] and cold atoms confined to 1-D tubes [3][4][5]. In higher dimensional systems, TLL is a tool that is often used, e.g. in edge theory [6] and coupled-wire constructions [7][8][9].

Topological transition on the conformal manifold

“…Since the two fermionic CFTs F and F differ by an IFTO, one may wonder if the domain wall between F and F contains a Majorana zero mode or not. This question can be approached by density-matrix renormalization-group theory [100], tensor networks [101], multi-scale entanglement renormalization ansatz (MERA) [102], or the conformal interface [80].…”

Charge density waves and their transitions in anisotropic quantum Hall systems

“…The overestimation gets corrected by increasing the bond dimension. One example is that a one-dimensional quasi-order leads to a finite-bond-dimension long-range order which decays with bond dimension [64][65][66] . In the current problem of QH CDW on an infinite cylinder, we find that translational symmetry breaking orders are overestimated; the 'rotational' symmetry breaking order is induced because of the finite bond dimension MPS.…”

Kinetic formation of trimers in a spinless fermionic chain

“…Forming trimers composed of a unique fermionic speciespin-polarized fermions -is particularly challenging despite seminal results in the context of the quantum Hall effect [34]. The pairing of spinless fermions already shows a rich phenomenology [35][36][37][38][39][40][41][42][43][44][45], and it is a crucial mechanism for some topological phases of matter, motivating further investigations in this direction. An intuitive route is to use attractive density interactions [42] on a chain and stabilize trimers using a third neighbor repulsion to prevent phase separation.…”

“…The pairing of spinless fermions already shows a rich phenomenology [35][36][37][38][39][40][41][42][43][44][45], and it is a crucial mechanism for some topological phases of matter, motivating further investigations in this direction. An intuitive route is to use attractive density interactions [42] on a chain and stabilize trimers using a third neighbor repulsion to prevent phase separation. In order to develop a low-energy description, as a trimer phase cannot be interpreted as an instability of the Luttinger liquid theory, the authors of Ref.…”

“…In order to develop a low-energy description, as a trimer phase cannot be interpreted as an instability of the Luttinger liquid theory, the authors of Ref. [42] propose an emergent-mode description, which is then treated with bosonisation tools. Unfortunately, such approach is not conclusive on the nature of the transition from the Luttinger liquid to the trimer phase.…”