Quantum criticality of loops with topologically constrained dynamics

Dai, Zhehao; Nahum, Adam

doi:10.1103/physrevresearch.2.033051

Cited by 12 publications

(8 citation statements)

References 40 publications

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“…We note that the fixed points of some quantum loop models were also proposed to be non-Lagrangian [123][124][125]. The nature of such loop quantum criticality appears to be very different from those studied in this paper.…”

Section: Discussioncontrasting

confidence: 52%

Stiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders

Zou,

He,

Wang

2021

Preprint

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We propose a new type of quantum liquids, dubbed Stiefel liquids, based on 2 + 1 dimensional nonlinear sigma models on target space SO(N )/SO(4), supplemented with Wess-Zumino-Witten terms. We argue that the Stiefel liquids form a class of critical quantum liquids with extraordinary properties, such as large emergent symmetries, a cascade structure, and nontrivial quantum anomalies. We show that the well known deconfined quantum critical point and U (1) Dirac spin liquid are unified as two special examples of Stiefel liquids, with N = 5 and N = 6, respectively. Furthermore, we conjecture that Stiefel liquids with N > 6 are non-Lagrangian, in the sense that under renormalization group they flow to infrared (conformally invariant) fixed points that cannot be described by any renormalizable continuum Lagrangian. Such non-Lagrangian states are beyond the paradigm of parton gauge theory familiar in the study of exotic quantum liquids in condensed matter physics. The intrinsic absence of (conventional or parton-like) mean-field construction also means that, within the traditional approaches, it will be difficult to decide whether a non-Lagrangian state can actually emerge from a specific UV system (such as a lattice spin system). For this purpose we hypothesize that a quantum state is emergible from a lattice system if its quantum anomalies match with the constraints from the (generalized) Lieb-Schultz-Mattis theorems. Based on this hypothesis, we find that some of the non-Lagrangian Stiefel liquids can indeed be realized in frustrated quantum spin systems, for example, on triangular or Kagome lattice, through the intertwinement between non-coplanar magnetic orders and valence-bond-solid orders. ContentsE. Explicit homomorphism between the su(4)and so(6) generators F. I (N ) anomalies of SL (N ) 1. The case with an even N a. The case with N = 2 (mod 4) b. The case with N = 0 (mod 4) 2. The case with an odd N G. More on the LSM constraints

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Section: Discussioncontrasting

confidence: 52%

Stiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders

Zou,

He,

Wang

2021

Preprint

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“…It would of course also be interesting to look for topologically constrained universality classes that do not have a classical correspondence. (There are also applications of the results of this paper to one-dimensional quantum systems, which we will discuss separately [34]. )…”

Section: Towards Other Topologically Constrained Modelsmentioning

confidence: 88%

“…Are there interesting gapless states adjacent to deconfined phases of gauge theories in 3+1D, where the flux lines have topologically constrained dynamics? (In a separate paper we will discuss a one-dimensional analogue of a topologically constrained model [34]. )…”

Section: Discussionmentioning

confidence: 99%

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Quantum criticality of loops with topologically constrained dynamics

Dai,

Nahum

2019

Preprint

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Quantum fluctuating loops in 2+1 dimensions give gapless many-body states that are beyond current field theory techniques. Microscopically, these loops can be domain walls between up and down spins, or chains of flipped spins similar to those in the toric code. The key feature of their dynamics is that reconnection of a pair of strands is forbidden. This happens at previously-studied multicritical points between topologically nontrivial phases. We show that this topologically constrained dynamics leads to universality classes with unusual scaling properties. For example, scaling operators at these fixed points are classified by topology, and not only by symmetry. We introduce the concept of the topological operator classification, provide universal scaling forms for correlation functions, and analytical and numerical results for critical exponents. We use an exact correspondence between the imaginary-time dynamics of the 2+1D quantum models and a classical Markovian dynamics for 2D classical loop models with a nonlocal Boltzmann weight (for which we also provide scaling results). We comment on open questions and generalizations of the models discussed for both quantum criticality and classical Markov processes.

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“…Loop models also give access to different kinds of operators that are less common in classical stat-mech problems. Particularly, watermelon correlators [6,[36][37][38][39] are important due to their relationship to anisotropy terms [40] and their quantum counterpart [41]. In 2D systems where conformal field theory works, there is a good understanding of the behaviour of these operators and their scaling dimension in some models.…”

Section: Introductionmentioning

confidence: 99%

3D Unoriented loop models and the $\mathrm{RP}^{n-1}$ sigma model

Serna

2021

Preprint

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We study a completely-packed loop model with crossings in a three-dimensional lattice and confirm it is described by RP n−1 sigma field theories. We use Monte Carlo simulations, with systems sizes up to 1800 × 1800 × 1800, to obtain the critical exponents for a universality class with no previously reported estimates in the literature, namely the replica-like limit n → 1 of RP n−1 sigma field theory. Classic critical exponents include ν = 0.918(5) and η = −0.091(9). We also provide estimates of the scaling dimension of the 4-legs watermelon correlators, particularly for n = 1 we obtain the value x4 = 1.292(8).

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Quantum criticality of loops with topologically constrained dynamics

Cited by 12 publications

References 40 publications

Stiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders

Stiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders

Quantum criticality of loops with topologically constrained dynamics

3D Unoriented loop models and the $\mathrm{RP}^{n-1}$ sigma model

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