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Density-Matrix Mean-Field Theory
by Junyi Zhang, Zhengqian Cheng
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Submission summary
| Authors (as registered SciPost users): | Junyi Zhang |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202406_00055v1 (pdf) |
| Date accepted: | 2024-07-09 |
| Date submitted: | 2024-06-24 15:07 |
| Submitted by: | Zhang, Junyi |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Mean-field theories have proven to be efficient tools for exploring diverse phases of matter, complementing alternative methods that are more precise but also more computationally demanding. Conventional mean-field theories often fall short in capturing quantum fluctuations, which restricts their applicability to systems with significant quantum effects. In this article, we propose an improved mean-field theory, density-matrix mean- field theory (DMMFT). DMMFT constructs effective Hamiltonians, incorporating quantum environments shaped by entanglements, quantified by the reduced density matrices. Therefore, it offers a systematic and unbiased approach to account for the effects of fluctuations and entanglements in quantum ordered phases. As demonstrative examples, we show that DMMFT can not only quantitatively evaluate the renormalization of order parameters induced by quantum fluctuations, but can also detect the topological quantum phases. Additionally, we discuss the extensions of DMMFT for systems at finite temperatures and those with disorders. Our work provides an efficient approach to explore phases exhibiting unconventional quantum orders, which can be particularly beneficial for investigating frustrated spin systems in high spatial dimensions.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
We are resubmitting our revised manuscript titled “Density-Matrix Mean-Field Theory” to SciPost Physics.
Following the previous round of review, the referee recommended minor revisions, which we have diligently addressed in this revision. Specifically, we have corrected imprecise usage of the terminology "integrable", enhanced figure resolution and captions, and conducted careful editorial checks. A detailed list of changes, directly addressing each of the referee's suggestions, is provided below.
We appreciate the editorial efforts of the journal team and look forward to the publication of our work in your esteemed journal.
Sincerely,
Junyi Zhang,
on behalf of the authors.
List of changes
1. Ref. Pt. 1.
We thank the referee for highlighting out our imprecise use of the terminology "integrable". Adopting referee's suggestion of reserving terminologies such as "integrable" or "exactly solvable" to models solvable in the Bethe-ansatz sense, we have revised our manuscript accordingly. We now refer to the β=1/3 point as "the special point of the AKLT model" or just explicitly state the value of β.
2. Ref. Pt. 2.
We adopt referee's suggestion of leaving the judgment of novelty to the readers. Accordingly, we have removed the word "novel" from the abstract and in our conclusion section.
3. Ref. Pt. 5 and Ref. Pt. 12 on more precise citations.
We appreciate referee's suggestions on more precise referring to the articles being cited.
(a) First paragraph of section 3: den Nijs and Rommelse’s paper previously cited as Ref. [68] in our earlier manuscript and now cited as Ref. [60] in this revised version. Both den Nijs and Rommelse’s paper, Ref. [60], and Pollmann and Turner’s paper, Ref. [61], are referenced for the string order.
(b) Page 13, four lines above the bottom: Chubukov and Golosov’s paper (cited as Ref. [54] in both our previous and revised manuscripts) is now cited alongside Ref. [52], tracking the historical development of the ideas of stabilizing the UUD state by quantum fluctuations.
4. Ref. Pt. 7.
We have updated Fig. 1 to include axis names for the horizontal axes, which represent the indices of the eigenvalues. Error bars are used to indicate the deviation of the DMMF results from the exact values. The caption has been revised to provide clearer clarification.
5. Ref. Pt. 10.
All figures in this revised manuscript have been re-exported to vector graphic format to ensure better resolutions.
6. Ref. Pts. 3, 4, 6, 8, 11, 13 -- 19.
We thank the referee for careful proofreading. We have conducted careful editorial checks, improved grammatic presentations, and corrected typos. Ref. Pts. 3, 4, 6, 8, 11, 13 -- 19 have been corrected.
Published as SciPost Phys. 17, 062 (2024)