We study the energy absorption in real time of a disordered quantum spin chain subjected to coherent monochromatic periodic driving. We determine characteristic fingerprints of the wellknown ergodic (Floquet-ETH for slow driving/weak disorder) and many-body localized (Floquet-MBL for fast driving/strong disorder) phases. In addition, we identify an intermediate regime, where the energy density of the system -unlike the entanglement entropy a local and bounded observable -grows logarithmically slowly over a very large time window.

Quantum spin systems are by now known to exhibit a large number of different classes of spin liquid phases. By contrast, for classical Heisenberg models, only one kind of fractionalised spin liquid phase, the so-called Coulomb or U (1) spin liquid, has until recently been identified: this exhibits algebraic spin correlations and impurity moments, 'orphan spins', whose size is a fraction of that of the underlying microscopic degrees of freedom. Here, we present two Heisenberg models exhibiting fractionalisation in combination with exponentially decaying correlations. These can be thought of as a classical continuous spin version of a Z2 spin liquid. Our work suggests a systematic search and classification of classical spin liquids as a worthwhile endeavour. PACS numbers:Fractionalisation is one of the several unusual properties generally observed in systems evading low temperature conventional symmetry breaking ordered states in favor of unconventional topological orders. On account of such exotic behavior, much attention has been devoted to the identification of systems exhibiting such new topological physics. Frustrated magnets [1][2][3] have played a prominent role, where several spin liquids (SL) [4,5] starting in the late 90s [6] were identified [7][8][9].While by now a multitude of quantum SL have been discovered [10] and classified [11], the situation with classical Heisenberg SL is comparatively much sparser. The first Heisenberg spin liquid to be identified unambiguously, the antiferromagnet on the pyrochlore lattice [7,12] is a U (1) spin liquid exhibiting pinch-points in its structure factor indicating algebraically decaying correlations [7,[12][13][14][15], as well as fractionalisation of its microscopic degrees of freedom: disorder in the form of dilution creates new, weakly-interacting, magnetic degrees of freedom which possess a half of the microscopic magnetic moments of the Heisenberg model [16,17].Such fractionalisation is perhaps the cleanest signature of spin-liquidity in such a classical setting, as definitions in terms of topological field theory are frustrated by the bulk gapless excitations due to the continuous classical nature of the Heisenberg spins.Given the by now overwhelming variety of known quantum spin liquids (for an example, see Ref. 18), it may therefore come as a surprise that no corresponding richness appears to exist for classical Heisenberg magnets: the U (1) case is the only one studied in detail. It turns up in many settings, such as the checkerboard and pyrochlore lattices (for n = 2 component spins) [7,12], the kagome (for n > 3 component spins) [19,20], or the SCGO 'pyrochlore slab' [21].Here we ask the question whether this absence of evidence of other types of spin liquid is evidence of absence. The answer is that there is indeed more diversity than has been so far recognised: we identify a new SL class which and a kagome (right) lattices. These can be respectively seen as fully connected squares forming a kagome, and fully connected hexagons forming a triangular, la...

We show that the honeycomb Heisenberg antiferromagnet with J1/2 = J2 = J3, where J 1/2/3 are first-, second-and third-neighbour couplings respectively, forms a classical spin liquid with pinch-point singularities in the structure factor at the Brillouin zone corners. Upon dilution with non-magnetic ions, fractionalised degrees of freedom carrying 1/3 of the free moment emerge. Their effective description in the limit of low-temperature is that of spins randomly located on a triangular lattice, with a frustrated interaction of long-ranged logarithmic form. The XY version of this magnet exhibits nematic thermal order by disorder, which comes with a clear experimental diagnostic. PACS numbers:Motivation.-The honeycomb lattice has -somewhat belatedly -become one of the prime hunting grounds for spin liquids (SL) in d = 2 [1], in addition to the kagome and the J 1 − J 2 square lattice Heisenberg models, which have been the focus of much attention over decades, continuing until today. In both these latter cases [2][3][4][5][6][7][8][9][10][11], confidence in the existence of a quantum SL state for S = 1/2 magnets has ebbed and flowed, while the classical (large-spin) versions evade liquidity by exhibitingrather interesting -forms of order by disorder [12][13][14][15][16][17][18][19][20].The richness of magnetic models on the honeycomb lattice -bipartite, like the square lattice -has therefore come as somewhat of a surprise. Initially emulating its brethren by appearing to support a quantum SL in a Hubbard model [21], it has been attracting attention in the context of the fractionalised phases of the Kitaev honeycomb model [22], exhibiting highly unusual exactly soluble quantum SL phases. Particular impetus arose from the suggestion that the Kitaev Hamiltonian may describe the materials {N a, Li} 2 IrO 3 , provided a Heisenberg term is added [23][24][25].In fact, detailed studies of these materials suggest that further nearest neighbor terms play an important role in explaining spiral ordering at low temperatures [26], and one of the models studied in some detail is the J 1 − J 2 − J 3 Heisenberg model, which had already been subject to considerable earlier attention [27][28][29][30]. In determining the Hamiltonian appropriate to these materials, it has turned out to be instructive to consider their response to disorder [31].Here, we identify and study in detail an unusual, hitherto overlooked, classical SL state on the honeycomb lattice, associated with the (known) degeneracy point J 1 /2 = J 2 = J 3 of the Heisenberg model on the honeycomb lattice. It exhibits remarkable new features. These arise from the fact that the dual lattice, as well as the underlying Bravais lattice, is the tripartite triangular lattice. They include pinch points in the structure factor at the zone corner wavevector Q (which distinguishes be-

We study a disordered classical Heisenberg magnet with uniformly antiferromagnetic interactions which are frustrated on account of their long-range Coulomb form, i.e. J(r) ∼ −A ln r in d = 2 and J(r) ∼ A/r in d = 3. This arises naturally as the T → 0 limit of the emergent interactions between vacancy-induced degrees of freedom in a class of diluted Coulomb spin liquids (including the classical Heisenberg antiferromagnets on checkerboard, SCGO and pyrochlore lattices) and presents a novel variant of a disordered long-range spin Hamiltonian. Using detailed analytical and numerical studies we establish that this model exhibits a very broad paramagnetic regime that extends to very large values of A in both d = 2 and d = 3. In d = 2, using the lattice-Green function based finite-size regularization of the Coulomb potential (which corresponds naturally to the underlying low-temperature limit of the emergent interactions between orphan-spins), we only find evidence that freezing into a glassy state occurs in the limit of strong coupling, A = ∞, while no such transition seems to exist at all in d = 3. We also demonstrate the presence and importance of screening for such a magnet. We analyse the spectrum of the Euclidean random matrices describing a Gaussian version of this problem, and identify a corresponding quantum mechanical scattering problem.