Real-Space Renormalization-Group Analysis of Random Quantum Spin Systems

Spin chains with quenched disorder exhibit rich critical behavior, often captured by real-space renormalization group (RSRG) techniques. However, the physics of such systems in the presence of random measurements (i.e., non-Hermitian dephasing) remains largely unexplored. The interplay between measurements and unitary dynamics gives rise to novel phases and phase transitions in monitored quantum systems. In this work, we investigate the disordered XX spin chain subject to stochastic local measurements in the $X$ and $Y$ bases. By mapping the monitored chain to a non-Hermitian spin ladder with complex couplings, we propose an RSRG-for-excited-states (RSRG-X) approach for this open-system setting. Our analysis reveals a new class of strongly disordered fixed points that emerge due to non-unitarity, broadening the landscape of critical phenomena accessible via RSRG.Spin chains with quenched disorder exhibit rich critical behavior, often captured by real-space renormalization group (RSRG) techniques. However, the physics of such systems in the presence of random measurements (i.e., non-Hermitian dephasing) remains largely unexplored. The interplay between measurements and unitary dynamics gives rise to novel phases and phase transitions in monitored quantum systems. In this work, we investigate the disordered XX spin chain subject to stochastic local measurements in the $X$ and $Y$ bases. By mapping the monitored chain to a non-Hermitian spin ladder with complex couplings, we propose an RSRG-for-excited-states (RSRG-X) approach for this open-system setting. Our analysis reveals a new class of strongly disordered fixed points that emerge due to non-unitarity, broadening the landscape of critical phenomena accessible via RSRG.

arXiv:2507.11957Physical review. B./Physical review. BFeb 26, 20261 citation

Random Quantum Spin Chains: A Real-Space Renormalization Group Study

E. Westerberg, Akira Furusaki, Manfred Sigrist +1 more

Quantum Heisenberg spin chains with random couplings and spin sizes are studied using a real-space renormalization group technique. These systems belong to a new universality class of disordered quantum spin systems realized in, e.g., ${\mathrm{Sr}}_{3}\mathrm{Cu}{\mathrm{Pt}}_{1\ensuremath{-}x}{\mathrm{Ir}}_{x}{\mathrm{O}}_{6}$. The low-energy fixed point is characterized by the formation of weakly coupled large effective spins. At low temperature $T$ the entropy obeys a power law ${T}^{\ensuremath{\delta}}$ ($\ensuremath{\delta}\ensuremath{\approx}0.44$), and the susceptibility follows a Curie-like behavior.Quantum Heisenberg spin chains with random couplings and spin sizes are studied using a real-space renormalization group technique. These systems belong to a new universality class of disordered quantum spin systems realized in, e.g., ${\mathrm{Sr}}_{3}\mathrm{Cu}{\mathrm{Pt}}_{1\ensuremath{-}x}{\mathrm{Ir}}_{x}{\mathrm{O}}_{6}$. The low-energy fixed point is characterized by the formation of weakly coupled large effective spins. At low temperature $T$ the entropy obeys a power law ${T}^{\ensuremath{\delta}}$ ($\ensuremath{\delta}\ensuremath{\approx}0.44$), and the susceptibility follows a Curie-like behavior.

arXiv:cond-mat/9507055Physical Review LettersDec 4, 199592 citations

Real-Space Renormalization-Group Method for Quantum Systems

Rémi Jullien, K. A. Penson, Pierre M. Pfeuty +1 more

Springer eBooksJan 1, 19800 citations

Study of Quantum Spin Systems using Real Space Renormalization Transformations

宏高野

物性研究Aug 20, 19790 citations

X

and

Y

bases. By mapping the monitored chain to a non-Hermitian spin ladder with complex couplings, we propose an RSRG-for-excited-states (RSRG-X) approach for this open-system setting. Our analysis reveals a new class of strongly disordered fixed points that emerge due to non-unitarity, broadening the landscape of critical phenomena accessible via RSRG.

T

the entropy obeys a power law ${T}^{\ensuremath{\delta}}$ ($\ensuremath{\delta}\ensuremath{\approx}0.44$), and the susceptibility follows a Curie-like behavior.