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arXiv:hep-lat/9902028 · Physical Review Letters

End States, Ladder Compounds, and Domain-Wall Fermions

Michael J. Creutz

Published Sep 27, 1999• 200 citations
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Abstract

A magnetic field applied to a cross-linked ladder compound can generate isolated electronic states bound to the ends of the chain. After exploring the interference phenomena responsible, I discuss a connection to the domain-wall approach to chiral fermions in lattice gauge theory. The robust nature of the states under small variations of the bond strengths is tied to chiral symmetry and the multiplicative renormalization of fermion masses.

DOI
10.1103/physrevlett.83.2636

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A magnetic field applied to a cross-linked ladder compound can generate isolated electronic states bound to the ends of the chain. After exploring the interference phenomena responsible, I discuss a connection to the domain-wall approach to chiral fermions in lattice gauge theory. The robust nature of the states under small variations of the bond strengths is tied to chiral symmetry and the multiplicative renormalization of fermion masses.
We report the experimental realization of a cross-linked chiral ladder with ultracold fermionic atoms in a 1D optical lattice. In the ladder, the legs are formed by the orbital states of the optical lattice and the complex interleg links are generated by the orbital-changing Raman transitions that are driven by a moving lattice potential superimposed onto the optical lattice. The effective magnetic flux per ladder plaquette is tuned by the spatial periodicity of the moving lattice, and the chiral currents are observed from the asymmetric momentum distributions of the orbitals. The effect of the complex cross-links is demonstrated in quench dynamics by measuring the momentum dependence of the interorbital coupling strength. We discuss the topological phase transition of the chiral ladder system for the variations of the complex cross-links.
When fermions are confined to move only in one dimension, as in a chain, then they form a Luttinger Liquid which differs fundamentally from the Landau Fermi Liquid that occurs in higher dimensions. If chains are combined to form ladders, one finds surprisingly that the properties of fermionic ladders depend essentially on their width. Ladder can be divided in two classes, those with odd and even numbers of legs. To date this behavior has been observed only in certain cuprate materials and the ideal of lightly doped and perfectly formed ladders has not been realized. The synthesis of materials with ladder structures should lead to interesting new physics.
Mesonic bound states of domain walls (DWs) can be stabilized in quasi-one-dimensional magnetic compounds. Here, we theoretically study the Raman light scattering response of a twisted Kitaev chain with tilted magnetic fields as a minimal model for confinement in CoNb2O6{\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}CoNb2​O6​. By both numerical matrix product states and few-DW variational states, we show that confinement-induced bound states directly manifest themselves as sharp peaks in the Raman response. Remarkably, by tuning the polarization of the incident light field, we demonstrate that the Raman response offers insights into the intrinsic symmetry of the bound-state wave function.
We study the particle spectrum M n ( h ) in the two-dimensional ferromagnetic Ising field theory in a weak external magnetic field h . According to the Wu and McCoy scenario of the weak confinement, pairs of fermions (domain walls) are coupled into bosonic kink–antikink bound states at small h > 0. Fluctuations with more than two fermions also contribute to the wavefunctions of the compound particles, leading to multi-fermion corrections to their masses M n ( h ) in higher orders in h . We describe a perturbative procedure, which allows us to account for both multi-fermion fluctuations and the long-range confining interaction between fermions, and leads to the formfactor expansions for the renormalized parameters of the model. We obtain integral representations for the third-order multi-fermion correction to the mass M n ( h ), which arises from the regular correction to the kernel of the Bethe–Salpeter equation.