Renormalization group study of the sliding Luttinger liquids

Sierra, Germȧn; Kim, Eugene H.

doi:10.1088/0305-4470/36/2/103

Cited by 7 publications

(9 citation statements)

References 11 publications

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“…4. Such a fixed point has also been found in the sliding Luttinger liquid perturbed by the vertex operators of dual fields [86]. Our result can be seen as an extension of their result to a two-component sliding Luttinger liquid.…”

Section: Appendix B: Renormalization Group Analysissupporting

confidence: 82%

Bridging coupled wires and lattice Hamiltonian for two-component bosonic quantum Hall states

Fuji

Bhattacharjee

et al. 2016

Phys. Rev. B

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We investigate a model of hard-core bosons with correlated hopping on the honeycomb lattice in an external magnetic field by means of a coupled-wire approach. It has been numerically shown that this model exhibits at half filling the bosonic integer quantum Hall (BIQH) state, which is a symmetry-protected topological phase protected by the U(1) particle conservation [Y.-C. He et al., Phys. Rev. Lett. 115, 116803 (2015)]. By combining the bosonization approach and a coupled-wire construction, we analytically confirm this finding and show that it even holds in the strongly anisotropic (quasi-one-dimensional) limit. We discuss the stability of the BIQH phase against tunnelings that break the separate particle conservations on different sublattices down to a global particle conservation. We further argue that a phase transition between two different BIQH phases is in a deconfined quantum critical point described by two copies of the (2 + 1)-dimensional O(4) nonlinear sigma model with the topological theta term at theta = pi. Finally, we predict a possible fractional quantum Hall state, the Halperin (221) state, at 1/6 filling

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Section: Appendix B: Renormalization Group Analysissupporting

confidence: 82%

Bridging coupled wires and lattice Hamiltonian for two-component bosonic quantum Hall states

Fuji

Bhattacharjee

et al. 2016

Phys. Rev. B

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“…Eq. ( 106) describes a Lie-algebraic generalization 70,71 of the self-dual sine-Gordon models considered in Ref. 72.…”

Section: A Case Of Four Competing Ordersmentioning

confidence: 99%

Competing orders and hidden duality symmetries in two-leg spin ladder systems

Lecheminant

Totsuka

2006

Phys. Rev. B

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A unifying approach to competing quantum orders in generalized two-leg spin ladders is presented. Hidden relationship and quantum phase transitions among the competing orders are thoroughly discussed by means of a low-energy field theory starting from an SU(4) quantum multicritical point. Our approach reveals that the system has a relatively simple phase structure in spite of its complicated interactions. On top of the U(1)symmetry which is known from previous studies to mixes up antiferromagnetic order parameter with that of the p-type nematic, we find an emergent U(1)-symmetry which mixes order parameters dual to the above. On the basis of the field-theoretical-and variational analysis, we give a qualitative picture for the global structure of the phase diagram. Interesting connection to other models (e.g. bosonic t-J model) is also discussed.

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“…Models similar to the one defined in eq. ( 38) have been studied in references [18,19,20,21], especially the self dual cases where g + = g − and when the perturbations of the gaussian model are relevant.…”

Section: B Bosonizationmentioning

confidence: 99%

Renormalization group limit cycles and field theories for ellipticS-matrices

LeClair

Sierra

2004

J. Stat. Mech.: Theor. Exp.

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The renormalization group for maximally anisotropic su(2) current interactions in 2d is shown to be cyclic at one loop. The fermionized version of the model exhibits spin-charge separation of the 4-fermion interactions and has Z Z4 symmetry. It is proposed that the S-matrices for these theories are the elliptic S-matrices of Zamolodchikov and Mussardo-Penati. The S-matrix parameters are related to lagrangian parameters by matching the period of the renormalization group. All models exhibit two characteristic signatures of an RG limit cycle: periodicity of the S-matrix as a function of energy and the existence of an infinite number of resonance poles satisfying Russian doll scaling.

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Renormalization group study of the sliding Luttinger liquids

Cited by 7 publications

References 11 publications

Bridging coupled wires and lattice Hamiltonian for two-component bosonic quantum Hall states

Bridging coupled wires and lattice Hamiltonian for two-component bosonic quantum Hall states

Competing orders and hidden duality symmetries in two-leg spin ladder systems

Renormalization group limit cycles and field theories for ellipticS-matrices

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