Combining quantum Monte Carlo simulations with the maximum entropy method, we study the dynamical structure factor $S(k,ω)$ of spin-1/2 antiferromagnetic Heisenberg chains with various random bond distributions. We emphasize the crossover behavior in the dynamical properties from pure chain to disorder-dominated random singlet phase due to bond randomness. For the distribution corresponding to the infinite randomness fixed point, $S(k,ω)$ develops broad non-spinon excitations as well as the random-singlet peak near $(k, ω) = (π, 0)$ , consistent with the known results obtained by the real-space renormalization group method. For weak disorder, however, we find clear signature of spinon excitations, reminiscent of pure spin chains, blurred by disorder. We discuss the implication for experiments on random-bond antiferromagnetic spin chains, realizable, e.g., in BaCu $_2$ (Si $_x$ Ge $_{1-x}$ ) $_2$ O $_7$ .Combining quantum Monte Carlo simulations with the maximum entropy method, we study the dynamical structure factor $S(k,ω)$ of spin-1/2 antiferromagnetic Heisenberg chains with various random bond distributions. We emphasize the crossover behavior in the dynamical properties from pure chain to disorder-dominated random singlet phase due to bond randomness. For the distribution corresponding to the infinite randomness fixed point, $S(k,ω)$ develops broad non-spinon excitations as well as the random-singlet peak near $(k, ω) = (π, 0)$, consistent with the known results obtained by the real-space renormalization group method. For weak disorder, however, we find clear signature of spinon excitations, reminiscent of pure spin chains, blurred by disorder. We discuss the implication for experiments on random-bond antiferromagnetic spin chains, realizable, e.g., in BaCu$_2$(Si$_x$Ge$_{1-x}$)$_2$O$_7$.

arXiv:cond-mat/0703772Mar 29, 20070 citations

Bound state and localization of excitation in many-body open systems

H. T. Cui, H. Z. Shen, S. C. Hou +1 more

We study the exact bound state and time evolution for single excitations in one-dimensional $XXZ$ spin chains within a non-Markovian reservoir. For the bound state, a common feature is the localization of single excitations, which means the spontaneous emission of excitations into the reservoir is prohibited. Exceptionally, the pseudo-bound state can be found, for which the single excitation has a finite probability of emission into the reservoir. In addition, a critical energy scale for bound states is also identified, below which only one bound state exists, and it is also the pseudo-bound state. The effect of quasirandom disorder in the spin chain is also discussed; such disorder induces the single excitation to locate at some spin sites. Furthermore, to display the effect of bound state and disorder on the preservation of quantum information, the time evolution of single excitations in spin chains is studied exactly. An interesting observation is that the excitation can stay at its initial location with high probability only when the bound state and disorder coexist. In contrast, when either one of them is absent, the information of the initial state can be erased completely or becomes mixed. This finding shows that the combination of bound state and disorder can provide an ideal mechanism for quantum memory.We study the exact bound state and time evolution for single excitations in one-dimensional $XXZ$ spin chains within a non-Markovian reservoir. For the bound state, a common feature is the localization of single excitations, which means the spontaneous emission of excitations into the reservoir is prohibited. Exceptionally, the pseudo-bound state can be found, for which the single excitation has a finite probability of emission into the reservoir. In addition, a critical energy scale for bound states is also identified, below which only one bound state exists, and it is also the pseudo-bound state. The effect of quasirandom disorder in the spin chain is also discussed; such disorder induces the single excitation to locate at some spin sites. Furthermore, to display the effect of bound state and disorder on the preservation of quantum information, the time evolution of single excitations in spin chains is studied exactly. An interesting observation is that the excitation can stay at its initial location with high probability only when the bound state and disorder coexist. In contrast, when either one of them is absent, the information of the initial state can be erased completely or becomes mixed. This finding shows that the combination of bound state and disorder can provide an ideal mechanism for quantum memory.

arXiv:1712.02506Physical Review AApr 30, 20188 citations

Measurement-induced phase transition in a disordered XX spin chain: A real-space renormalization group study

Siddharth Tiwary, Joel E. Moore

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

Slow Propagation in Some Disordered Quantum Spin Chains

Bruno Nachtergaele, Jake Reschke

arXiv:1906.10167Journal of Statistical PhysicsJan 1, 20217 citations

Combining quantum Monte Carlo simulations with the maximum entropy method, we study the dynamical structure factor

S(k,ω)

of spin-1/2 antiferromagnetic Heisenberg chains with various random bond distributions. We emphasize the crossover behavior in the dynamical properties from pure chain to disorder-dominated random singlet phase due to bond randomness. For the distribution corresponding to the infinite randomness fixed point,

S(k,ω)

develops broad non-spinon excitations as well as the random-singlet peak near

(k, ω) = (π, 0)

, consistent with the known results obtained by the real-space renormalization group method. For weak disorder, however, we find clear signature of spinon excitations, reminiscent of pure spin chains, blurred by disorder. We discuss the implication for experiments on random-bond antiferromagnetic spin chains, realizable, e.g., in BaCu

_2

(Si

_x

_{1-x}

)

_2

_7

We study the exact bound state and time evolution for single excitations in one-dimensional

XXZ

spin chains within a non-Markovian reservoir. For the bound state, a common feature is the localization of single excitations, which means the spontaneous emission of excitations into the reservoir is prohibited. Exceptionally, the pseudo-bound state can be found, for which the single excitation has a finite probability of emission into the reservoir. In addition, a critical energy scale for bound states is also identified, below which only one bound state exists, and it is also the pseudo-bound state. The effect of quasirandom disorder in the spin chain is also discussed; such disorder induces the single excitation to locate at some spin sites. Furthermore, to display the effect of bound state and disorder on the preservation of quantum information, the time evolution of single excitations in spin chains is studied exactly. An interesting observation is that the excitation can stay at its initial location with high probability only when the bound state and disorder coexist. In contrast, when either one of them is absent, the information of the initial state can be erased completely or becomes mixed. This finding shows that the combination of bound state and disorder can provide an ideal mechanism for quantum memory.

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.