CONFINEMENT AND QUANTUM ANOMALY IN QUASI-1D SPINLESS FERMION CHAINS

We consider the field renormalization group (RG) of two coupled one-spatial dimension (1D) spinless fermion chains under intraforward, interforward, interbackscattering and interumklapp interactions until two-loops order. Up to this order, we demonstrate the quantum confinement in the RG flow, where the interband chiral Fermi points reduce to single chiral Fermi points and the renormalized interaction couplings have Luttinger liquid fixed points. We show that this quasi-1D system is equivalently described in terms of one- and two-color interactions and address the problem of quantum anomaly, inherent to this system, as a direct consequence of coupling 1+1 free Dirac fields to one- and two-color interactions.

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Superdiffusive transport of energy in one-dimensional metals

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1916213117 ◽

2020 ◽

Vol 117 (23) ◽

pp. 12713-12718

Author(s):

Vir B. Bulchandani ◽

Christoph Karrasch ◽

Joel E. Moore

Keyword(s):

Ballistic Transport ◽

Luttinger Liquid ◽

Spatial Dimension ◽

Matrix Product ◽

Time Resolved ◽

One Dimensional ◽

Matrix Product State ◽

Spinless Fermion ◽

Free Theory ◽

Superdiffusive Transport

Metals in one spatial dimension are described at the lowest energy scales by the Luttinger liquid theory. It is well understood that this free theory, and even interacting integrable models, can support ballistic transport of conserved quantities including energy. In contrast, realistic one-dimensional metals, even without disorder, contain integrability-breaking interactions that are expected to lead to thermalization and conventional diffusive linear response. We argue that the expansion of energy when such a nonintegrable Luttinger liquid is locally heated above its ground state shows superdiffusive behavior (i.e., spreading of energy that is intermediate between diffusion and ballistic propagation), by combining an analytical anomalous diffusion model with numerical matrix-product–state calculations on a specific perturbed spinless fermion chain. Different metals will have different scaling exponents and shapes in their energy spreading, but the superdiffusive behavior is stable and should be visible in time-resolved experiments.

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Emergent chiral symmetry in a three-dimensional interacting Dirac liquid

Journal of High Energy Physics ◽

10.1007/jhep01(2021)004 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

András L. Szabó ◽

Bitan Roy

Keyword(s):

Fixed Points ◽

Chiral Symmetry ◽

Rotational Symmetry ◽

Three Dimensional ◽

Spatial Dimension ◽

Dirac Fermions ◽

Electronic Interactions ◽

Emergent Phenomena ◽

Ordered Phases ◽

The Stability

Abstract We compute the effects of strong Hubbardlike local electronic interactions on three-dimensional four-component massless Dirac fermions, which in a noninteracting system possess a microscopic global U(1) ⊗ SU(2) chiral symmetry. A concrete lattice realization of such chiral Dirac excitations is presented, and the role of electron-electron interactions is studied by performing a field theoretic renormalization group (RG) analysis, controlled by a small parameter ϵ with ϵ = d−1, about the lower-critical one spatial dimension. Besides the noninteracting Gaussian fixed point, the system supports four quantum critical and four bicritical points at nonvanishing interaction couplings ∼ ϵ. Even though the chiral symmetry is absent in the interacting model, it gets restored (either partially or fully) at various RG fixed points as emergent phenomena. A representative cut of the global phase diagram displays a confluence of scalar and pseudoscalar excitonic and superconducting (such as the s-wave and p-wave) mass ordered phases, manifesting restoration of (a) chiral U(1) symmetry between two excitonic masses for repulsive interactions and (b) pseudospin SU(2) symmetry between scalar or pseudoscalar excitonic and superconducting masses for attractive interactions. Finally, we perturbatively study the effects of weak rotational symmetry breaking on the stability of various RG fixed points.

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Renormalization group theory of molecular dynamics

Scientific Reports ◽

10.1038/s41598-021-85286-3 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Daiji Ichishima ◽

Yuya Matsumura

Keyword(s):

Molecular Dynamics ◽

Renormalization Group ◽

Critical Exponent ◽

Computational Efficiency ◽

Large Scale ◽

Dissipative Particle Dynamics ◽

Computational Cost ◽

Coarse Graining ◽

Spatial Dimension ◽

Deborah Number

AbstractLarge scale computation by molecular dynamics (MD) method is often challenging or even impractical due to its computational cost, in spite of its wide applications in a variety of fields. Although the recent advancement in parallel computing and introduction of coarse-graining methods have enabled large scale calculations, macroscopic analyses are still not realizable. Here, we present renormalized molecular dynamics (RMD), a renormalization group of MD in thermal equilibrium derived by using the Migdal–Kadanoff approximation. The RMD method improves the computational efficiency drastically while retaining the advantage of MD. The computational efficiency is improved by a factor of $$2^{n(D+1)}$$ 2 n ( D + 1 ) over conventional MD where D is the spatial dimension and n is the number of applied renormalization transforms. We verify RMD by conducting two simulations; melting of an aluminum slab and collision of aluminum spheres. Both problems show that the expectation values of physical quantities are in good agreement after the renormalization, whereas the consumption time is reduced as expected. To observe behavior of RMD near the critical point, the critical exponent of the Lennard-Jones potential is extracted by calculating specific heat on the mesoscale. The critical exponent is obtained as $$\nu =0.63\pm 0.01$$ ν = 0.63 ± 0.01 . In addition, the renormalization group of dissipative particle dynamics (DPD) is derived. Renormalized DPD is equivalent to RMD in isothermal systems under the condition such that Deborah number $$De\ll 1$$ D e ≪ 1 .

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Mapping the Spinless Fermion-Boson Model onto a Luttinger Liquid Model

Chinese Physics Letters ◽

10.1088/0256-307x/13/11/001 ◽

1996 ◽

Vol 13 (11) ◽

pp. 801-804 ◽

Cited By ~ 1

Author(s):

Yu-peng Wang ◽

Fu-ke Pu

Keyword(s):

Luttinger Liquid ◽

Spinless Fermion ◽

Liquid Model ◽

Boson Model

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PERTURBED W3 CONFORMAL THEORIES AND SPIN-4/3 PARAFERMIONIC COSET MODELS

Modern Physics Letters A ◽

10.1142/s0217732391002670 ◽

1991 ◽

Vol 06 (25) ◽

pp. 2281-2287 ◽

Cited By ~ 1

Author(s):

R. B. MANN ◽

H. B. ZHENG

Keyword(s):

Renormalization Group ◽

Fixed Points ◽

Renormalization Group Flows ◽

Coset Models

Renormalization group flows in W3, conformal theories are analyzed in relation to the ones in spin-4/3 parafermionic coset models and some of the operator content for new fixed points is identified.

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