Generalized Haldane map from the matrix product state path integral to the critical theory of the J_{1}-J_{2} chain
We study the J_{1}-J_{2} spin-1/2 chain using a path integral constructed over matrix product states (MPS). By virtue of its nontrivial entanglement structure, the MPS ansatz captures the key phases of the model even at a semiclassical, saddle-point level, and, as a variational state, is in good agr...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2025-02-01
|
| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.7.L012037 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849721147877228544 |
|---|---|
| author | F. Azad Adam J. McRoberts Chris Hooley A. G. Green |
| author_facet | F. Azad Adam J. McRoberts Chris Hooley A. G. Green |
| author_sort | F. Azad |
| collection | DOAJ |
| description | We study the J_{1}-J_{2} spin-1/2 chain using a path integral constructed over matrix product states (MPS). By virtue of its nontrivial entanglement structure, the MPS ansatz captures the key phases of the model even at a semiclassical, saddle-point level, and, as a variational state, is in good agreement with the field theory obtained by Abelian bosonization. Going beyond the semiclassical level, we show that the MPS ansatz facilitates a physically motivated derivation of the field theory of the critical phase: By carefully taking the continuum limit—a generalization of the Haldane map—we recover from the MPS path integral a field theory with the correct topological term and emergent SO(4) symmetry, constructively linking the microscopic states and topological field-theoretic structures. Moreover, the dimerization transition is particularly clear in the MPS formulation—an explicit dimerization potential becomes relevant, gapping out the magnetic fluctuations. |
| format | Article |
| id | doaj-art-9c6221e0c4cd4b30be2b48ad1e817fc2 |
| institution | DOAJ |
| issn | 2643-1564 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj-art-9c6221e0c4cd4b30be2b48ad1e817fc22025-08-20T03:11:46ZengAmerican Physical SocietyPhysical Review Research2643-15642025-02-0171L01203710.1103/PhysRevResearch.7.L012037Generalized Haldane map from the matrix product state path integral to the critical theory of the J_{1}-J_{2} chainF. AzadAdam J. McRobertsChris HooleyA. G. GreenWe study the J_{1}-J_{2} spin-1/2 chain using a path integral constructed over matrix product states (MPS). By virtue of its nontrivial entanglement structure, the MPS ansatz captures the key phases of the model even at a semiclassical, saddle-point level, and, as a variational state, is in good agreement with the field theory obtained by Abelian bosonization. Going beyond the semiclassical level, we show that the MPS ansatz facilitates a physically motivated derivation of the field theory of the critical phase: By carefully taking the continuum limit—a generalization of the Haldane map—we recover from the MPS path integral a field theory with the correct topological term and emergent SO(4) symmetry, constructively linking the microscopic states and topological field-theoretic structures. Moreover, the dimerization transition is particularly clear in the MPS formulation—an explicit dimerization potential becomes relevant, gapping out the magnetic fluctuations.http://doi.org/10.1103/PhysRevResearch.7.L012037 |
| spellingShingle | F. Azad Adam J. McRoberts Chris Hooley A. G. Green Generalized Haldane map from the matrix product state path integral to the critical theory of the J_{1}-J_{2} chain Physical Review Research |
| title | Generalized Haldane map from the matrix product state path integral to the critical theory of the J_{1}-J_{2} chain |
| title_full | Generalized Haldane map from the matrix product state path integral to the critical theory of the J_{1}-J_{2} chain |
| title_fullStr | Generalized Haldane map from the matrix product state path integral to the critical theory of the J_{1}-J_{2} chain |
| title_full_unstemmed | Generalized Haldane map from the matrix product state path integral to the critical theory of the J_{1}-J_{2} chain |
| title_short | Generalized Haldane map from the matrix product state path integral to the critical theory of the J_{1}-J_{2} chain |
| title_sort | generalized haldane map from the matrix product state path integral to the critical theory of the j 1 j 2 chain |
| url | http://doi.org/10.1103/PhysRevResearch.7.L012037 |
| work_keys_str_mv | AT fazad generalizedhaldanemapfromthematrixproductstatepathintegraltothecriticaltheoryofthej1j2chain AT adamjmcroberts generalizedhaldanemapfromthematrixproductstatepathintegraltothecriticaltheoryofthej1j2chain AT chrishooley generalizedhaldanemapfromthematrixproductstatepathintegraltothecriticaltheoryofthej1j2chain AT aggreen generalizedhaldanemapfromthematrixproductstatepathintegraltothecriticaltheoryofthej1j2chain |