SciPost Submission Page
Continuously varying critical exponents in long-range quantum spin ladders
by Patrick Adelhardt, Kai Phillip Schmidt
This is not the latest submitted version.
This Submission thread is now published as
|Authors (as registered SciPost users):||Patrick Adelhardt|
|Preprint Link:||scipost_202301_00041v1 (pdf)|
|Date submitted:||2023-01-31 10:13|
|Submitted by:||Adelhardt, Patrick|
|Submitted to:||SciPost Physics|
We investigate the quantum-critical behavior between the rung-singlet phase with hidden string order and the N\'eel phase with broken SU(2)-symmetry in quantum spin ladders with algebraically decaying unfrustrated long-range Heisenberg interactions. To this end, we determine high-order series expansions of energies and observables in the thermodynamic limit about the isolated rung-dimer limit. This is achieved by extending the method of perturbative continuous unitary transformations (pCUT) to long-range Heisenberg interactions and to the calculation of generic observables. The quantum-critical breakdown of the rung-singlet phase then allows us to determine the critical phase transition line and the entire set of critical exponents as a function of the decay exponent of the long-range interaction. We demonstrate long-range mean-field behavior as well as a non-trivial regime of continuously varying critical exponents implying the absence of deconfined criticality contrary to a recent suggestion in the literature.
Submission & Refereeing History
You are currently on this page
Reports on this Submission
1) Considers a class of systems of growing importance
2) Reports valid results for critical exponents
1) Nothing very striking or surprising is reported
There is a growing interest in quantum spin models with long-range
(power-law decaying) interactions - for both experimental and more
theoretical reasons. This paper presents a useful contribution in
this area, using high-order expansions around the rung limit of a
The main aim here is to compute critical exponents of the system
at the transition between the ordered Neel phase and the rung
singlet phase. The exponents vary with the interaction parameters
and results that appear stable/reliable are obtained. The work
is carried out carefully, even considering the log corrections
when the system is effectively at the upper critical dimension.
I do not think any of the results are particularly striking or
surprising, but overall they are certainly useful. One of the
main conclusions is that a previous claim of deconfined criticality
 does not seem to hold up. If I understand correctly, this
conclusion is based on the result that the dynamic exponent is
not one. Here I note that the true nature of the deconfined
criticality has come under renewed scrutiny, and it is not
completely clear what transitions should even fall under this
umbrella - perhaps z=1 is not even required and there are some
works showing transitions that are at least in some way related
to deconfined criticality but where Lorentz invariance is broken
(e.g., PRB 104, 045110 (2021) and previous papers where a spin
liquid connected to a dqc point are discussed). Discussing
these recent developments may go a bit too far from the topic
of the paper but I wanted to point it out for consideration
by the authors in case there is something else in their
results that could support (or not) the deconfined criticality
scenario beyond z not being one. The authors do point out
that the rung singlet phase is trivial, which in itself seems
to suggest that no unusual mechanisms need to be invoked.
The paper can be published after the authors have considered
the above suggestion (any changes are optional). I recommend that
the authors also check the English one more time; while the paper
overall reads very well, there are some minor errors, e.g., the
line after Eq. (2), where "distant-dependence" should be
Report 1 by Nicolas Laflorencie on 2023-4-14 (Invited Report)
1- Interesting and well-posed physical problem
2- Results are quantitative and go beyond the state of the art
3- Technical details well balanced with the results and their interpretation
1- Lack of experimental relevance/discussion
2- Some confusion between T=0 and finite T HMW theorem
This paper addresses interesting quantum critical phenomena in long-range spin ladders using a combination of large-S (spin-wave) calculations and PCUT calculations. Overall the results are quite convincing, although not exact, as opposed to feasible (frustration-free) quantum Monte Carlo simulations. Nevertheless, the authors find that a deconfined criticality scenario is not present, contrasting with previous claims. The phase diagrams and estimates for critical exponents are obtained, and well presented.
Phase diagrams: it may have been useful to superimpose with models in order to ease their comparison. The SW value at infinite \lambda is not clearly explained (it ressembles a symbols)
Critical exponents: The plots do not show with enough clarity the departure from MF behaviors. The readability should be improved for Figs. 3 and 4. When comparing with Ref.  where \eta and z have been computed along the non-MF critical line, the behaviors are quite different. Indeed in the preprint the authors find \eta \le (2-\sigma) and z\ge \sigma/2. If one translates onto the notations of Ref.  where the regime \sigma\ge 1 was studied, it was found that \eta \ge 2-\sigma and z\le 1 (see Figs. 9 and 10 in ). Of course the nature of the transition here is different: the critical line separates LRO from a gapped state (in contrast with  where the transition is LRO -QLRO). It would be interesting to comment on this, in particular if such an observed behavior could be an artifact of the PCUT technique? Does it make sense to try to study this model with QMC?
In any case the present study is a really interesting work that clearly deserves publication.
I have a few additional minor comments to make.
First, I think the discussion about the Mermin-Wagner theorem is a bit misleading in the introduction. Mermin-Wagner does not say anything about T=0 LRO, but only about finite T (note that MW has been improved by Bruno, your Ref , stating that finite T LRO can occur if \sigma<1 ). The only work that I know addressing the T=0 case is [Néel order in the ground state of Heisenberg antiferromagnetic chains with long-range interactions, byRodrigo Parreira, O Bolina and J Fernando Perez, J. Phys. A 30, 1095 (1997)].
Talking about possible deconfined quantum criticality, probably better candidates would be frustrated models. How would PCUT perform if instead on the unfrustrated ladder, one would take for instance the J1-J2 two-leg ladder? See Phys. Rev. B 73, 214427 (2006) or Phys. Rev. B 84, 144407 (2011).
Finally, do you have in mind some possible experimental relevance for this setup? It would be interesting to motivate a bit more on this aspect.
1- The discussion about HMW theorem
2- Improvement on the readability of the critical exponents figures