We study the antiferromagnetic XYZ spin chain with quenched bond randomness, focusing on a critical line between localized Ising magnetic phases. A previous calculation using the spectrum-bifurcation renormalization group, and assuming marginal many-body localization, proposed that critical indices vary continuously. In this work, we solve the low-energy physics using an unbiased numerically exact tensor network method named the ``rigorous renormalization group.'' We find a line of fixed points consistent with infinite-randomness phenomenology, with indeed continuously varying critical exponents for average spin correlations. A self-consistent Hartree--Fock-type treatment of the $z$ couplings as interactions added to the free-fermion random XY model captures much of the important physics including the varying exponents; we provide an understanding of this as a result of local correlation induced between the mean-field couplings. We solve the problem of the locally correlated XY spin chain with an arbitrary degree of correlation and provide analytical strong-disorder renormalization group proofs of continuously varying exponents based on an associated classical random walk problem. This is also an example of a line of fixed points with continuously varying exponents in the equivalent disordered free-fermion chain. We argue that this line of fixed points also controls an extended region of the critical interacting XYZ spin chain.We study the antiferromagnetic XYZ spin chain with quenched bond randomness, focusing on a critical line between localized Ising magnetic phases. A previous calculation using the spectrum-bifurcation renormalization group, and assuming marginal many-body localization, proposed that critical indices vary continuously. In this work, we solve the low-energy physics using an unbiased numerically exact tensor network method named the ``rigorous renormalization group.'' We find a line of fixed points consistent with infinite-randomness phenomenology, with indeed continuously varying critical exponents for average spin correlations. A self-consistent Hartree--Fock-type treatment of the $z$ couplings as interactions added to the free-fermion random XY model captures much of the important physics including the varying exponents; we provide an understanding of this as a result of local correlation induced between the mean-field couplings. We solve the problem of the locally correlated XY spin chain with an arbitrary degree of correlation and provide analytical strong-disorder renormalization group proofs of continuously varying exponents based on an associated classical random walk problem. This is also an example of a line of fixed points with continuously varying exponents in the equivalent disordered free-fermion chain. We argue that this line of fixed points also controls an extended region of the critical interacting XYZ spin chain.

arXiv:2107.12937Physical review. B./Physical review. BDec 27, 20219 citations

Critical Exponents of the Heisenberg Spin Chain

Jill C. Bonner, Gerhard H. Muller

Physical Review LettersApr 14, 19865 citations

Disordered XYZ spin chain simulations using the spectrum bifurcation renormalization group

Kevin Slagle, Yi‐Zhuang You, Cenke Xu

We study the disordered XYZ spin chain using the recently developed spectrum bifurcation renormalization group [Y.-Z. You et al., Phys. Rev. B 93, 104205 (2016)] numerical method. With strong disorder, the phase diagram consists of three many-body localized (MBL) spin-glass phases. We argue that, with sufficiently strong disorder, these spin-glass phases are separated by marginally MBL critical lines. We examine the critical lines of this model by measuring the entanglement entropy and Edwards-Anderson spin-glass order parameter, and find that the critical lines are characterized by an effective central charge ${c}^{\ensuremath{'}}=ln2$. Our data also suggest continuously varying critical exponents along the critical lines. We also demonstrate how long-range mutual information [introduced in C.-M. Jian et al., arXiv:1508.07006] can distinguish these phases.We study the disordered XYZ spin chain using the recently developed spectrum bifurcation renormalization group [Y.-Z. You et al., Phys. Rev. B 93, 104205 (2016)] numerical method. With strong disorder, the phase diagram consists of three many-body localized (MBL) spin-glass phases. We argue that, with sufficiently strong disorder, these spin-glass phases are separated by marginally MBL critical lines. We examine the critical lines of this model by measuring the entanglement entropy and Edwards-Anderson spin-glass order parameter, and find that the critical lines are characterized by an effective central charge ${c}^{\ensuremath{'}}=ln2$. Our data also suggest continuously varying critical exponents along the critical lines. We also demonstrate how long-range mutual information [introduced in C.-M. Jian et al., arXiv:1508.07006] can distinguish these phases.

arXiv:1604.04283Physical review. B./Physical review. BJul 15, 201621 citations

Energy transport in a disordered spin chain with broken U(1) symmetry: Diffusion, subdiffusion, and many-body localization

Maximilian Schulz, Scott R. Taylor, C. Hooley +1 more

We explore the physics of the disordered XYZ spin chain using two complementary numerical techniques: exact diagonalization (ED) on chains of up to 17 spins, and time-evolving block decimation (TEBD) on chains of up to 400 spins. Our principal findings are as follows. First, we verify that the clean XYZ spin chain shows ballistic energy transport for all parameter values that we investigated. Second, for weak disorder there is a stable diffusive region that persists up to a critical disorder strength that depends on the XY anisotropy. Third, for disorder strengths above this critical value, energy transport becomes increasingly subdiffusive. Fourth, the many-body localization transition moves to significantly higher disorder strengths as the XY anisotropy is increased. We discuss these results, and their relation to our current physical picture of subdiffusion in the approach to many-body localization.We explore the physics of the disordered XYZ spin chain using two complementary numerical techniques: exact diagonalization (ED) on chains of up to 17 spins, and time-evolving block decimation (TEBD) on chains of up to 400 spins. Our principal findings are as follows. First, we verify that the clean XYZ spin chain shows ballistic energy transport for all parameter values that we investigated. Second, for weak disorder there is a stable diffusive region that persists up to a critical disorder strength that depends on the XY anisotropy. Third, for disorder strengths above this critical value, energy transport becomes increasingly subdiffusive. Fourth, the many-body localization transition moves to significantly higher disorder strengths as the XY anisotropy is increased. We discuss these results, and their relation to our current physical picture of subdiffusion in the approach to many-body localization.

arXiv:1805.01036Physical review. B./Physical review. BNov 5, 201839 citations

CRITICAL EXPONENTS OF MIXED QUANTUM SPIN CHAIN

R. BISCHOF, Wolfhard Janke E

International Conference on Path IntegralsNov 1, 20080 citations

z

couplings as interactions added to the free-fermion random XY model captures much of the important physics including the varying exponents; we provide an understanding of this as a result of local correlation induced between the mean-field couplings. We solve the problem of the locally correlated XY spin chain with an arbitrary degree of correlation and provide analytical strong-disorder renormalization group proofs of continuously varying exponents based on an associated classical random walk problem. This is also an example of a line of fixed points with continuously varying exponents in the equivalent disordered free-fermion chain. We argue that this line of fixed points also controls an extended region of the critical interacting XYZ spin chain.