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arXiv:2309.01652 · Physical review. B./Physical review. B

Emergent self-duality in a long-range critical spin chain: From deconfined criticality to first-order transition

Sheng Yang, Zhiming Pan, Da-Chuan Lu, Xue-Jia Yu

Published Dec 21, 2023• 11 citations
arXivHTMLPDF

Abstract

Over the past few decades, tremendous efforts have been devoted to understanding self-duality at the quantum critical point, which enlarges the global symmetry and constrains the dynamics. A one-dimensional spin chain is an ideal platform for the theoretical investigation of these exotic phenomena, due to powerful simulation methods such as the density matrix renormalization group. Deconfined quantum criticality with self-duality at the critical point has been found in an extended short-range spin chain. In this work, we employ large-scale density matrix renormalization group simulations to investigate a critical spin chain with long-range power-law interaction $V(r)\ensuremath{\sim}1/{r}^{\ensuremath{\alpha}}$. Remarkably, we reveal that the long-range interaction drives the original deconfined criticality towards a first-order phase transition as $\ensuremath{\alpha}$ decreases. More strikingly, the emergent self-duality leads to an enlarged symmetry and manifests at these first-order critical points. This discovery is reminiscent of self-duality protected multicritical points, and it provides an example of the critical line with generalized symmetry. Our work has far-reaching implications for ongoing experimental efforts in Rydberg atom quantum simulators.

DOI
10.1103/physrevb.108.245152

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Over the past few decades, tremendous efforts have been devoted to understanding self-duality at the quantum critical point, which enlarges the global symmetry and constrains the dynamics. A one-dimensional spin chain is an ideal platform for the theoretical investigation of these exotic phenomena, due to powerful simulation methods such as the density matrix renormalization group. Deconfined quantum criticality with self-duality at the critical point has been found in an extended short-range spin chain. In this work, we employ large-scale density matrix renormalization group simulations to investigate a critical spin chain with long-range power-law interaction V(r)\ensuremath∼1/r\ensuremathαV(r)\ensuremath{\sim}1/{r}^{\ensuremath{\alpha}}V(r)\ensuremath∼1/r\ensuremathα. Remarkably, we reveal that the long-range interaction drives the original deconfined criticality towards a first-order phase transition as \ensuremathα\ensuremath{\alpha}\ensuremathα decreases. More strikingly, the emergent self-duality leads to an enlarged symmetry and manifests at these first-order critical points. This discovery is reminiscent of self-duality protected multicritical points, and it provides an example of the critical line with generalized symmetry. Our work has far-reaching implications for ongoing experimental efforts in Rydberg atom quantum simulators.
Duality places an important constraint on the renormalization group flows and the phase diagrams. For self-dual theories, the self-duality can be promoted as a symmetry, this leads to the multicriticalities. This work investigates a description of the deconfined quantum criticality, the Nf=2QED3{N}_{f}=2\phantom{\rule{4pt}{0ex}}{\mathrm{QED}}_{3}Nf​=2QED3​, as an example of self-dual theories, and its multicritical behavior under perturbative deformations. The multicriticality is described by the theory with Gross-Neveu couplings and falls in a different universality class than the standard deconfined quantum criticality. We systematically calculate the scaling dimensions of various operators in the 3D quantum electrodynamics with the Chern-Simons term and Gross-Neveu couplings by the large-NNN renormalization group analysis. Specifically, we find certain Drelativistic four-fermion interactions which correspond to the dimer-dimer interactions in the lattice model will drive the deconfined quantum criticality to the first-order transition, this result is consistent with previous numerical studies.
The deconfined quantum critical point (QCP), separating the Néel and valence bond solid phases in a 2D antiferromagnet, was proposed as an example of (2+1)D criticality fundamentally different from standard Landau-Ginzburg-Wilson-Fisher criticality. In this work, we present multiple equivalent descriptions of deconfined QCPs, and use these to address the possibility of enlarged emergent symmetries in the low-energy limit. The easy-plane deconfined QCP, besides its previously discussed self-duality, is dual to N_{f}=2 fermionic quantum electrodynamics, which has its own self-duality and hence may have an O(4)×Z_{2}^{T} symmetry. We propose several dualities for the deconfined QCP with SU(2) spin symmetry which together make natural the emergence of a previously suggested SO(5) symmetry rotating the Néel and valence bond solid orders. These emergent symmetries are implemented anomalously. The associated infrared theories can also be viewed as surface descriptions of (3+1)D topological paramagnets, giving further insight into the dualities. We describe a number of numerical tests of these dualities. We also discuss the possibility of “pseudocritical” behavior for deconfined critical points, and the meaning of the dualities and emergent symmetries in such a scenario.
Abstract Long-range interactions in one-dimensional quantum systems can qualitatively modify low-energy critical behavior and provide a natural setting for exploring unconventional phase transitions beyond short-range Tomonaga—Luttinger liquid physics. In this work, we study a one-dimensional XXZ spin chain with transverse long-range interactions and an explicit dimerization perturbation. Using bosonization and weak-coupling renormalization group (RG) analysis, we derive the RG flow equations. The resulting weak-coupling phase diagram contains a gapless Tomonaga—Luttinger liquid, an explicitly dimerized phase, and a continuous symmetry breaking (CSB) phase induced by the transverse long-range interaction. We further analyze the collapse point at which the two perturbations become simultaneously marginal. A stability analysis of the corresponding doubly marginal Gaussian fixed point shows that it is weakly unstable rather than a stable multicritical infrared fixed point, thereby giving rise to a pseudo-multicritical crossover over large length scales. Similar physics may be accessible in Rydberg-atom systems, offering a controllable theoretical and experimental platform for exploring long-range interaction effects and crossover behavior in one-dimensional quantum systems.
The deconfined phase of (2+12+12+1)-dimensional Zk{\mathbb{Z}}_{k}Zk​ gauge theory exhibits topological order, with eee and mmm anyons that have a $2\ensuremath{\pi}/k$ braiding phase. Proliferating either eee or mmm drives Higgs or confinement transitions, respectively. At the multicritical point where these transitions meet, the theory enjoys an additional duality symmetry that exchanges eee and mmm anyons. This symmetry forces anyons with nontrivial braiding to close their gaps simultaneously, giving rise to a critical theory that mixes strong interactions with mutual statistics. We propose an effective $\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ gauge theory with a mutual Chern-Simons term at level kkk to describe the vicinity of the multicritical point for $k\ensuremath{\ge}4$. The emergence of a global $\mathrm{U}{(1)}^{\mathrm{top}}\ifmmode\times\else\texttimes\fi{}\mathrm{U}{(1)}^{\mathrm{top}}$ symmetry at the critical point imposes powerful constraints on universal properties of the phase transition. In particular, we show that (1) the lattice magnetic flux operator embeds as a conserved U(1) current with protected scaling dimension; (2) the first-order line emanating from the critical point for k=2k=2k=2 disappears generically for sufficiently large kkk; (3) the correlation length exponent approaches that of the three-dimensional XY model with corrections of order 1/k21/{k}^{2}1/k2 in the large-kkk limit. These predictions can be tested in near-term numerical simulations and pave the way for a more general exploration of topological quantum criticality enriched with anyon-permuting symmetries.
We study a generalized quantum spin ladder with staggered long range interactions that decay as a power-law with exponent α\alphaα. Using the density matrix renormalization group (DMRG) method and exact diagonalization, we show that this model undergoes a transition from a rung-dimer phase characterized by a non-local string order parameter, to a symmetry broken Neel phase at αc∼2.1\alpha_c\sim 2.1αc​∼2.1. We find evidence that the transition is second order with a dynamic critical exponent z=1z=1z=1 and ν≈1.2\nu\approx 1.2ν≈1.2. In the magnetically ordered phase, the spectrum exhibits gapless modes, while excitations in the gapped phase are well described in terms of triplons -- bound states of spinons across the legs. We obtained the momentum resolved spin dynamic structure factor numerically and found that the triplon band is well defined at high energies and adiabatically connected to the magnon dispersion. However, at low energies it emerges as the lower edge of continuum of excitations that shifts to high energies across the transition. We further discuss the possibility of deconfined criticality in this model.
The spontaneous breaking of noninvertible symmetries can lead to exotic phenomena such as the coexistence of order and disorder. Here, we explore second-order phase transitions in one-dimensional spin chains between two phases that correspond to distinct patterns of noninvertible symmetry breaking. The critical point shares several features with well-understood examples of deconfined quantum critical points, such as enlarged symmetry and identical exponents for the two order parameters participating in the transition. Interestingly, such deconfined transitions involving noninvertible symmetries allow one to construct a whole family of similar critical points by gauging spin-flip symmetries. By employing gauging and bosonization, we characterize the phase diagram of our model in the vicinity of the critical point. We also explore proximate phases and phase transitions in related models, including a deconfined quantum critical point between invertible order parameters that is enforced by a noninvertible symmetry.