Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2205.06829 · Physical review. B./Physical review. B

Spin- and flux-gap renormalization in the random Kitaev spin ladder

Wen-Han Kao, Natalia Borisovna Perkins

Published Sep 9, 2022• 7 citations
arXivHTMLPDF

Abstract

We study the Kitaev spin ladder with random couplings by using the real-space strong-disorder renormalization group (SDRG) technique. This model is the minimum model in Kitaev systems that has conserved plaquette fluxes, and its quasi-one-dimensional geometry makes it possible to study the strong-disorder fixed points for both spin- and flux-excitation gaps. In the Ising limit where the $x$-type Ising couplings compete with the $z$-type couplings and the $y$-type couplings are small but nonzero, the behavior of the spin gap is consistent with a random transverse-field Ising chain, but the flux gap is dominated by the $y$-type couplings. In the XX limit, while the $x$- and $y$-type couplings are locally equal and renormalized simultaneously, the $z$-type couplings are not renormalized drastically and lead to nonuniversal disorder criticality at low-energy scales. We show that different types of fractionalized degrees of freedom in the disordered Kitaev model can result in different critical behaviors, as long as its fluxes can survive the perturbative treatment.

DOI
10.1103/physrevb.106.l100402

Related papers

Transverse spin correlations of the random transverse-field Ising model

Ferenc Iglói, István A. Kovács

The critical behavior of the random transverse-field Ising model in finite-dimensional lattices is governed by infinite disorder fixed points, several properties of which have already been calculated by the use of the strong disorder renormalization-group (SDRG) method. Here we extend these studies and calculate the connected transverse-spin correlation function by a numerical implementation of the SDRG method in $d=1,2$, and 3 dimensions. At the critical point an algebraic decay of the form $\ensuremath{\sim}{r}^{\ensuremath{-}{\ensuremath{\eta}}_{t}}$ is found, with a decay exponent being approximately ${\ensuremath{\eta}}_{t}\ensuremath{\approx}2+2d$. In $d=1$ the results are related to dimer-dimer correlations in the random antiferromagnetic $XX$ chain and have been tested by numerical calculations using free-fermionic techniques.

arXiv:1712.07467•Physical review. B./Physical review. B•Mar 21, 2018•4 citations

Emergent glassiness in the disorder-free Kitaev model: Density matrix renormalization group study on a one-dimensional ladder setting

K. B. Yogendra, Tanmoy Das, G. Baskaran

The complete phase diagram of the Kitaev model with a magnetic field remains elusive, as do the experimental results in the candidate material $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$. Here, we study the Kitaev model on a one-dimensional ladder setting within the density-matrix renormalization group method in the presence of a magnetic field at zero temperature. We find five distinct phases with increasing magnetic field, which are characterized by a homogeneous flux phase, the ${Z}_{2}$ vortex gas, solid and emergent glass phase, and finally, a spin-polarized phase. The emergent glassiness is confirmed by calculating correlation functions showing quasi-long-range behavior and ground state fidelity, showing a plethora of energetically accessible orthogonal saddle points corresponding to different flux configurations. This glassy behavior seems to arise from the slow dynamics of the ${Z}_{2}$ fluxes, which is a consequence of the local constraints present in the underlying Hilbert space. This phenomenon can also be explored in other spin-liquid systems where the corresponding low-energy excitations are similarly retarded due to constraints.

arXiv:2302.14328•Physical review. B./Physical review. B•Oct 12, 2023•13 citations

Critical behavior and entanglement of the random transverse-field Ising model between one and two dimensions

István A. Kovács, Ferenc Iglói

We consider disordered ladders of the transverse-field Ising model and study their critical properties and entanglement entropy for varying width, $w\ensuremath{\le}20$, by numerical application of the strong disorder renormalization group method. We demonstrate that the critical properties of the ladders for any finite $w$ are controlled by the infinite disorder fixed point of the random chain and the correction to scaling exponents contain information about the two-dimensional model. We calculate sample dependent pseudocritical points and study the shift of the mean values as well as scaling of the width of the distributions and show that both are characterized by the same exponent, $\ensuremath{\nu}(2d)$. We also study scaling of the critical magnetization, investigate critical dynamical scaling as well as the behavior of the critical entanglement entropy. Analyzing the $w$ dependence of the results we have obtained accurate estimates for the critical exponents of the two-dimensional model: $\ensuremath{\nu}(2d)=1.25(8)$, $x(2d)=0.996(15)$, and $\ensuremath{\psi}(2d)=0.51(3)$.

arXiv:0909.4442•Physical Review B•Dec 17, 2009•46 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.

arXiv:2507.11957•Physical review. B./Physical review. B•Feb 26, 2026•1 citation

Renormalization group study of the two-dimensional random transverse-field Ising model

István A. Kovács, Ferenc Iglói

The infinite-disorder fixed point of the random transverse-field Ising model is expected to control the critical behavior of a large class of random quantum and stochastic systems having an order parameter with discrete symmetry. Here we study the model on the square lattice with a very efficient numerical implementation of the strong disorder renormalization group method, which makes us possible to treat finite samples of linear size up to $L=2048$. We have calculated sample dependent pseudocritical points and studied their distribution, which is found to be characterized by the same shift and width exponent: $\ensuremath{\nu}=1.24(2)$. For different types of disorder the infinite-disorder fixed point is shown to be characterized by the same set of critical exponents, for which we have obtained improved estimates: $x=0.982(15)$ and $\ensuremath{\psi}=0.48(2)$. We have also studied the scaling behavior of the magnetization in the vicinity of the critical point as well as dynamical scaling in the ordered and disordered Griffiths phases.

arXiv:1005.4740•Physical Review B•Aug 31, 2010•105 citations

Strong-disorder renormalization-group study of the one-dimensional tight-binding model

H. Javan Mard, José A. Hoyos, E. Miranda +1 more

We formulate a strong-disorder renormalization-group (SDRG) approach to study the $\ensuremath{\beta}$ function of the tight-binding model in one dimension with both diagonal and off-diagonal disorder for states at the band center. We show that the SDRG method, when used to compute transport properties, yields exact results since it is identical to the transfer matrix method. The $\ensuremath{\beta}$ function is shown to be universal when only off-diagonal disorder is present even though single-parameter scaling is known to be violated. A different single-parameter scaling theory is formulated for this particular (particle-hole symmetric) case. Upon breaking particle-hole symmetry (by adding diagonal disorder), the $\ensuremath{\beta}$ function is shown to crossover from the universal behavior of the particle-hole symmetric case to the conventional nonuniversal one in agreement with the two-parameter scaling theory. We finally draw an analogy with the random transverse-field Ising chain in the paramagnetic phase. The particle-hole symmetric case corresponds to the critical point of the quantum Ising model, while the generic case corresponds to the Griffiths paramagnetic phase.

arXiv:1404.1381•Physical Review B•Sep 23, 2014•21 citations
We study the Kitaev spin ladder with random couplings by using the real-space strong-disorder renormalization group (SDRG) technique. This model is the minimum model in Kitaev systems that has conserved plaquette fluxes, and its quasi-one-dimensional geometry makes it possible to study the strong-disorder fixed points for both spin- and flux-excitation gaps. In the Ising limit where the xxx-type Ising couplings compete with the zzz-type couplings and the yyy-type couplings are small but nonzero, the behavior of the spin gap is consistent with a random transverse-field Ising chain, but the flux gap is dominated by the yyy-type couplings. In the XX limit, while the xxx- and yyy-type couplings are locally equal and renormalized simultaneously, the zzz-type couplings are not renormalized drastically and lead to nonuniversal disorder criticality at low-energy scales. We show that different types of fractionalized degrees of freedom in the disordered Kitaev model can result in different critical behaviors, as long as its fluxes can survive the perturbative treatment.
The critical behavior of the random transverse-field Ising model in finite-dimensional lattices is governed by infinite disorder fixed points, several properties of which have already been calculated by the use of the strong disorder renormalization-group (SDRG) method. Here we extend these studies and calculate the connected transverse-spin correlation function by a numerical implementation of the SDRG method in d=1,2d=1,2d=1,2, and 3 dimensions. At the critical point an algebraic decay of the form $\ensuremath{\sim}{r}^{\ensuremath{-}{\ensuremath{\eta}}_{t}}$ is found, with a decay exponent being approximately ${\ensuremath{\eta}}_{t}\ensuremath{\approx}2+2d$. In d=1d=1d=1 the results are related to dimer-dimer correlations in the random antiferromagnetic XXXXXX chain and have been tested by numerical calculations using free-fermionic techniques.
The complete phase diagram of the Kitaev model with a magnetic field remains elusive, as do the experimental results in the candidate material $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$. Here, we study the Kitaev model on a one-dimensional ladder setting within the density-matrix renormalization group method in the presence of a magnetic field at zero temperature. We find five distinct phases with increasing magnetic field, which are characterized by a homogeneous flux phase, the Z2{Z}_{2}Z2​ vortex gas, solid and emergent glass phase, and finally, a spin-polarized phase. The emergent glassiness is confirmed by calculating correlation functions showing quasi-long-range behavior and ground state fidelity, showing a plethora of energetically accessible orthogonal saddle points corresponding to different flux configurations. This glassy behavior seems to arise from the slow dynamics of the Z2{Z}_{2}Z2​ fluxes, which is a consequence of the local constraints present in the underlying Hilbert space. This phenomenon can also be explored in other spin-liquid systems where the corresponding low-energy excitations are similarly retarded due to constraints.
We consider disordered ladders of the transverse-field Ising model and study their critical properties and entanglement entropy for varying width, $w\ensuremath{\le}20$, by numerical application of the strong disorder renormalization group method. We demonstrate that the critical properties of the ladders for any finite www are controlled by the infinite disorder fixed point of the random chain and the correction to scaling exponents contain information about the two-dimensional model. We calculate sample dependent pseudocritical points and study the shift of the mean values as well as scaling of the width of the distributions and show that both are characterized by the same exponent, $\ensuremath{\nu}(2d)$. We also study scaling of the critical magnetization, investigate critical dynamical scaling as well as the behavior of the critical entanglement entropy. Analyzing the www dependence of the results we have obtained accurate estimates for the critical exponents of the two-dimensional model: $\ensuremath{\nu}(2d)=1.25(8)$, x(2d)=0.996(15)x(2d)=0.996(15)x(2d)=0.996(15), and $\ensuremath{\psi}(2d)=0.51(3)$.
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 XXX and YYY 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.
The infinite-disorder fixed point of the random transverse-field Ising model is expected to control the critical behavior of a large class of random quantum and stochastic systems having an order parameter with discrete symmetry. Here we study the model on the square lattice with a very efficient numerical implementation of the strong disorder renormalization group method, which makes us possible to treat finite samples of linear size up to L=2048L=2048L=2048. We have calculated sample dependent pseudocritical points and studied their distribution, which is found to be characterized by the same shift and width exponent: $\ensuremath{\nu}=1.24(2)$. For different types of disorder the infinite-disorder fixed point is shown to be characterized by the same set of critical exponents, for which we have obtained improved estimates: x=0.982(15)x=0.982(15)x=0.982(15) and $\ensuremath{\psi}=0.48(2)$. We have also studied the scaling behavior of the magnetization in the vicinity of the critical point as well as dynamical scaling in the ordered and disordered Griffiths phases.
We formulate a strong-disorder renormalization-group (SDRG) approach to study the $\ensuremath{\beta}$ function of the tight-binding model in one dimension with both diagonal and off-diagonal disorder for states at the band center. We show that the SDRG method, when used to compute transport properties, yields exact results since it is identical to the transfer matrix method. The $\ensuremath{\beta}$ function is shown to be universal when only off-diagonal disorder is present even though single-parameter scaling is known to be violated. A different single-parameter scaling theory is formulated for this particular (particle-hole symmetric) case. Upon breaking particle-hole symmetry (by adding diagonal disorder), the $\ensuremath{\beta}$ function is shown to crossover from the universal behavior of the particle-hole symmetric case to the conventional nonuniversal one in agreement with the two-parameter scaling theory. We finally draw an analogy with the random transverse-field Ising chain in the paramagnetic phase. The particle-hole symmetric case corresponds to the critical point of the quantum Ising model, while the generic case corresponds to the Griffiths paramagnetic phase.