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Deconfined Quantum Criticality in the longrange, anisotropic Heisenberg Chain
by Anton Romen, Stefan Birnkammer, Michael Knap
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Submission summary
Authors (as registered SciPost users):  Stefan Birnkammer · Michael Knap · Anton Romen 
Submission information  

Preprint Link:  https://arxiv.org/abs/2311.06350v1 (pdf) 
Date submitted:  20231114 11:29 
Submitted by:  Romen, Anton 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approaches:  Theoretical, Computational 
Abstract
Deconfined quantum criticality describes continuous phase transitions that are not captured by the LandauGinzburg paradigm. Here, we investigate deconfined quantum critical points in the longrange, anisotropic Heisenberg chain. With matrix product state simulations, we show that the model undergoes a continuous phase transition from a valence bond solid to an antiferromagnet. We extract the critical exponents of the transition and connect them to an effective field theory obtained from bosonization techniques. We show that beyond stabilizing the valance bond order, the longrange interactions are irrelevant and the transition is well described by a double frequency sineGordon model. We propose how to realize and probe deconfined quantum criticality in our model with trappedion quantum simulators.
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Reports on this Submission
Anonymous Report 2 on 20231220 (Invited Report)
 Cite as: Anonymous, Report on arXiv:2311.06350v1, delivered 20231220, doi: 10.21468/SciPost.Report.8316
Strengths
Scaling analysis is carefully done to show convincing numerical evidence for deconfined quantum criticality in the longrange, anisotropic Heisenberg chain.
Report
This paper discusses deconfined quantum criticality between the valence bond solid (VBS) ground state and the antiferromagnetic (AFM) ground state in the longrange anisotropic Heisenberg chain, using matrix product state simulations and bosonization methods.
The phase diagram is obtained from the numerical simulations in the twoparameter space of the exponent $\alpha$ of the longrange interaction ($\propto 1/r^\alpha$) and the exchange anisotropy $\Delta$, and the phase boundary between the VBS and AFM phases is determined for $\alpha>1$. Through a careful scaling analysis with varying bond dimensions $\chi$, the phase transition is shown to be continuous, with the central charge $c=1$ obtained from the scaling of entanglement entropy.
The lowenergy effective theory for the phase transition is derived using bosonization, reproducing the previous theory in Refs. [10,24]. An important new result in this derivation is that the longrange part of the exchange interactions (beyond the nextnearestneighbor interactions discussed in [10,24]) is irrelevant in the renormalizationgroup sense.
The critical exponents $\beta_{\rm VBS}$ and $\beta_{\rm AFM}$ for the VBS and AFM order parameters and the correlation length exponent $\nu$ are also estimated from the numerical simulations. While it turns out to be difficult to determine the individual scaling exponents with good accuracy, the scaling analysis of the residual order parameters at critical points due to finite bond dimensions allows the authors to successfully obtain a good agreement between the critical exponents ratio $\beta/\nu$ and the Luttinger parameter $K$ in support of the effective theory.
Finally, a proposal is made for realizing and observing, with trappedion quantum simulators, the deconfined quantum criticality in the theoretical model studied in this paper.
The results of this paper summarized above are reasonable and valid, and the proposal might stimulate experimental studies. The manuscript is well written and easy to read. I can therefore recommend this paper for publication in SciPost Physics.
Anonymous Report 1 on 20231219 (Invited Report)
 Cite as: Anonymous, Report on arXiv:2311.06350v1, delivered 20231219, doi: 10.21468/SciPost.Report.8314
Strengths
1. Clear presentation of the results.
2. Motivation comes from recent experimental realization of spin chain with longrange interactions.
3. Numerical results complemented and supported by field theoretical techniques.
4. Agreement between critical exponents for different order parameters provides compelling evidence for a 1D deconfined quantum critical point.
Weaknesses
1. The results do not offer any fundamentally new insight because the same transition has been studied in very closely related models, both by bosonization and by DMRG.
2. The section about experimental prospects essentially repeats the proposal and analysis from Ref. [12].
Report
Anisotropic spin chains with frustrated interactions beyond nearest neighbors have been studied in recent years in the context of 1D analogs of deconfined quantum criticality; see e.g. Refs. [6] and [10]. In this context, the present manuscript investigates the continuous transition from antiferromagnetic (AFM) to valence bond solid (VBS) order in a spin chain model with powerlawdecaying interactions that can be realized experimentally (Ref. [13]). The authors combine numerical (iDMRG) methods with a standard bosonization analysis to show that the transition is described by an effective field theory with central charge c=1 (a Luttinger liquid). They also extract the Luttinger parameter from its relation to critical exponents. Within the limitations associated with the finite bond dimension used in the iDMRG simulations, the results are consistent with the field theory predictions.
The sineGordon theory for the transition in Eq. (7) has been extensively discussed in the literature; see e.g. Refs. [10] and [12]. In fact, if the longrange interactions are truncated at nextnearest neighbors, the Hamiltonian in Eq. (1) reduces to the one studied by Mudry et al. in Ref. [10], where both bosonization and DMRG methods were used to characterize the transition. In section 4 the authors argue that the longrange contributions do not modify the essential physics as long as the exponent \alpha is large enough. Indeed, the AFMVBS transition was also studied using very similar methods in a model with longrange interactions in Ref. [12]. In contrast with Ref. [12], where the exponent was fixed to correspond to dipolar and Van der Waals interactions, in this manuscript the authors vary the exponent between \alpha=1 and \alpha=2, but the results are qualitatively the same. The discussion in section 6 about detecting the emergent U(1) symmetry at the critical point using snapshots of the order parameters is also very similar to what was done in Ref. [12].
In my opinion, this manuscript does not present groundbreaking discoveries or breakthroughs in comparison with previous results in the literature. Therefore, it does not meet the expectations listed in the acceptance criteria of SciPost Physics, but it could be published in SciPost Physics Core.
Requested changes
1. When discussing the limits of the model in Sec. 2, I suggest citing papers that considered the isotropic limit before Ref. [15], for instance Parreira et al., J. Phys. A 30, 1095 (1997); Laflorencie et al., J. Stat. Mech. P12001 (2005).
2. In the paragraph above Eq. (6), I believe the authors meant to say that they considered nearest and nextnearest neighbor interactions (not only nextnearest).
3. Please define K as the Luttinger parameter right below Eq. (7), where it first appears.
4. Please write the value of \alpha in the caption of Fig. 2.