Emergent chiral symmetry in a three-dimensional interacting Dirac liquid

Szabo, Andras; Roy, Bitan

doi:10.48550/arxiv.2009.05055

Cited by 2 publications

(2 citation statements)

References 30 publications

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“…Emergent symmetries in quantum critical systems have been the subject of numerous recent discussions in condensed matter physics [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and more generally in quantum field theory [20][21][22][23] and the conformal bootstrap [24][25][26]. An emergent symmetry is often associated with a length scale ξ above which the symmetry is violated as a consequence of a so-called dangerously irrelevant (DI) perturbation close to a continuous phase transition [27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Unconventional U(1) to $\mathbf{Z_q}$ cross-over in quantum and classical ${\bf q}$-state clock models

Patil,

Shao,

Sandvik

2020

Preprint

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We consider two-dimensional q-state quantum clock models with quantum fluctuations connecting states with all-to-all clock transitions with different choices for the matrix elements. We study the quantum phase transitions in these models using quantum Monte Carlo simulations and finite-size scaling, with the aim of characterizing the cross-over from emergent U(1) symmetry at the transition (for q ≥ 4) to Zq symmetry of the ordered state. We also study classical three-dimensional clock models with spatial anisotropy corresponding to the space-time anisotropy of the quantum systems. The U(1) to Zq symmetry cross-over in all these systems is governed by a so-called dangerously irrelevant operator. We specifically study q = 5 and q = 6 models with different forms of the quantum fluctuations and different anisotropies in the classical models. In all cases, we find the expected classical XY critical exponents and scaling dimensions yq of the clock fields. However, the initial weak violation of the U(1) symmetry in the ordered phase, characterized by a Zq symmetric order parameter φq, scales in an unexpected way. As a function of the system size (length) L, close to the critical temperature φq ∝ L p , where the known value of the exponent is p = 2 in the classical isotropic clock model. In contrast, for strongly anisotropic classical models and the quantum models we find p = 3. For weakly anisotropic classical models we observe a cross-over from p = 2 to p = 3 scaling. The exponent p directly impacts the exponent ν governing the divergence of the U(1) to Zq cross-over length scale ξ in the thermodynamic limit, according to the relationship ν = ν(1 + |yq|/p), where ν is the conventional correlation length exponent. We present a phenomenological argument for p = 3 based on an anomalous renormalization of the clock field in the presence of anisotropy, possibly as a consequence of topological (vortex) line defects. Thus, our study points to an intriguing interplay between conventional and dangerously irrelevant perturbations, which may affect also other quantum systems with emergent symmetries.

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Section: Introductionmentioning

confidence: 99%

Unconventional U(1) to $\mathbf{Z_q}$ cross-over in quantum and classical ${\bf q}$-state clock models

Patil,

Shao,

Sandvik

2020

Preprint

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“…In order to justify potential types of symmetry breaking, we are suggested to bring out the following source terms that collect both the charge and spin channels 11,45,48,106…”

Section: Instabilities Induced By Fermion-fermion Interactionsmentioning

confidence: 99%

Fermion-fermion interaction driven instability and criticality of quadratic band crossing systems with the breaking of time-reversal symmetry

Zhai,

Wang

2020

Preprint

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Roles of fermion-fermion interactions are carefully studied in governing the low-energy fates of a two-dimensional spin-1/2 fermionic system on the kagomé lattice, which features a quadratic band crossing point touched parabolically by up and down energy bands. In the framework of a renormalization group, we establish the coupled energy-dependent flows of fermionic interaction parameters by treating all kinds of fermionic interactions on the same footing and unbiasedly taking into account their one-loop corrections. Through a compressive analysis of these evolutions that carry the hierarchical information of physics, a number of outlandish behaviors are progressively decoded and addressed manifestly in the low-energy regime. At first, we find that various sorts of fermion-fermion interactions furiously compete and affect each other. With the decrease of energy scale, they are inevitably attracted by certain fixed point in the parameter space which clusters into three qualitatively distinct regions relying heavily upon structure parameters of materials. In addition, the leading instability accompanied by some symmetry breaking is attentively investigated in the proximity of different sorts of fixed points. Computing and comparing susceptibilities of twelve potential candidates indicates that charge density wave always dominates over others. Incidently, there exists several options for subleading ones including the x-current, bond density, and chiral plus s-wave superconductors. At last, we examine how physical observables behave nearby the dominant instability. Due to the strong fluctuations neighboring this instability linked to charge density wave, density of states and specific heat as well compressibility of quasiparticles are significantly suppressed, signalling the emergence of non-Fermi liquid behaviors.

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Emergent chiral symmetry in a three-dimensional interacting Dirac liquid

Cited by 2 publications

References 30 publications

Unconventional U(1) to $\mathbf{Z_q}$ cross-over in quantum and classical ${\bf q}$-state clock models

Unconventional U(1) to $\mathbf{Z_q}$ cross-over in quantum and classical ${\bf q}$-state clock models

Fermion-fermion interaction driven instability and criticality of quadratic band crossing systems with the breaking of time-reversal symmetry

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