We investigate the zero-temperature phase diagram of a one-dimensional XXZ spin chain coupled with local dissipative baths composed of simple harmonic oscillators. In a finite magnetization sector, we map this system onto a two-dimensional classical action using bosonization. From this classical field theory, we find the existence of a BKT phase transition between the pre-existing Luttinger liquid phase and a new dissipative phase at zero temperature. This new phase is a gapless spin density wave with unaltered susceptibility and vanishing spin stiffness. These analytical predictions are verified against numerical Langevin dynamics simulations of the action. The local baths in the spin chain can also be interpreted as annealed disorder and they affect the transport properties. Particularly for subohmic baths, the static conductivity vanishes, which can be interpreted as a localization effect induced by the presence of dynamical disorder. Moreover, we analyze the model at zero magnetization and argue that in that case, the gapless spin density wave is replaced by a gapped antiferromagnetic phase.
Authors
- Bibliographic Reference
- Saptarshi Majumdar. Localization in Open Quantum Systems. Disordered Systems and Neural Networks [cond-mat.dis-nn]. Université Paris-Saclay, 2023. English. ⟨NNT : 2023UPASP157⟩. ⟨tel-04326573⟩
- HAL Collection
- ["CEA - Commissariat à l'énergie atomique", 'CNRS - Centre national de la recherche scientifique', 'STAR - Dépôt national des thèses électroniques', 'IPHT', 'CEA - Université Paris-Saclay', 'Université Paris-Saclay', 'Direction de Recherche Fondamentale', 'Graduate School Mathématiques', 'Graduate School Physique', 'Laboratoire de Physique Théorique et Modèles Statistiques']
- HAL Identifier
- 4326573
- Institution
- ['Université Paris-Saclay', "Commissariat à l'énergie atomique et aux énergies alternatives"]
- Laboratory
- ['Laboratoire de Physique Théorique et Modèles Statistiques', 'Institut de Physique Théorique - UMR CNRS 3681']
- Published in
- France
Table of Contents
- Acknowledgment 7
- Introduction 9
- Open Quantum Systems 13
- Model 17
- Microscopic model 18
- Jordan-Wigner transformation 20
- Bosonization and Field theory 23
- Bosonization of 1D XXZ spin chain 24
- Non-interacting hamiltonian 24
- Interacting part 28
- Effective action: Path integral and integrating out the baths 30
- Luttinger liquid and sine-Gordon model 33
- Methods 36
- Perturbative Renormalization Group 36
- Renormalization Group of Sine-Gordon model 37
- Variational ansatz 39
- Theory 40
- Example: Sine-Gordon model 41
- Langevin dynamics 44
- The Incommensurate case: Phase diagram 47
- RG analysis of the Incommensurate case 48
- Derivation of the RG flow equation 48
- Analysis of the RG flow equations 51
- Variational analysis 54
- Dissipative phase 56
- LL phase 58
- Numerical solution of the self-consistent equation 60
- Phase diagram 61
- The Incommensurate case: Thermodynamics and Transport 63
- Thermodynamical properties 64
- Susceptibility 64
- Statistical Tilt Symmetry 66
- Order Parameter 68
- LL phase 70
- Dissipative phase 71
- Behaviour of the order parameter 71
- Spin-spin correlation 73
- Spatial spin-spin correlation 73
- Imaginary time spin-spin correlation 74
- Nature of the dissipative phase 76
- Dynamical properties: Conductivity and Charge stiffness 76
- LL phase 78
- Dissipative phase 79
- Charge stiffness 80
- Numerical results 80
- Discussion 84
- Commensurate Phase 87
- Variational analysis 88
- Phase diagram 90
- Numerical Results 91
- Discussion 94
- Conclusions 96
- Publications 98
- Résumé en Français 120
- Details of Bosonization 126
- Commutation of density fluctuation operators 126
- Exact form of the bosonic operators 127
- Details of Path Integral and Correlation functions 129
- Gaussian integral over complex variable 129
- Behaviour of roughness function in the LL phase 130
- Correlation of exponential functions 133
- Numerical methods 135
- Supplementary Results 138
