Abstract
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 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.
Highlights
In many situations, phases of many-body quantum systems are stable under weak static, or “quenched,” disorder in the presence of a gap, and the disorder average of certain quantities can be calculated in a related clean system via either the replica trick or supersymmetry arguments for noninteracting models [1,2]
We investigate a modern application of real-space RG to a random XYZ spin chain [3,4], where we use exact numerics to perform unbiased exploration and validation, and use the strong-disorder renormalization group (SDRG) to demonstrate and characterize such fixed points using the language of random walks
Our objective is primarily to verify by unbiased numerics the observation of continuously varying critical exponents in the spectrum bifurcation renormalization group” (SBRG) study of [4], and to shed additional light on the nature of the low-energy theory. (Here we focus solely on the ground state properties and low-energy physics, rather than the question of many-body localization (MBL).) For concreteness, we use the disorder distribution described in Eqs. (3) and (4) of Ref. [4], namely, p Jiα =
Summary
Phases of many-body quantum systems are stable under weak static, or “quenched,” disorder in the presence of a gap, and the disorder average of certain quantities can be calculated in a related clean system via either the replica trick or supersymmetry arguments for noninteracting models [1,2]. As a brief overview of our results, the data found by RRG are in support of both infinite-randomness physics as well as continuously varying critical indices for disorder-averaged correlations These conclusions are based on direct measurements in MPS, along with scaling of low-energy spectral gaps, which we solve for in the various symmetry sectors of the model up to systems of length N = 80 spins. Returning to the interacting model, based on the above understanding of the noninteracting case and the RRG numerical data, we conjecture that at least in the neighborhood of the free-fermion model, interactions are irrelevant and the local correlations generated in the SDRG drive the interacting theory to the line of noninteracting IRFPs at long distances
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