Quantum spin circulator in Y junctions of Heisenberg chains

Abstract

We show that a quantum spin circulator, a nonreciprocal device that routes spin currents without any charge transport, can be achieved in Y junctions of identical spin-1/2 Heisenberg chains coupled by a chiral three-spin interaction. Using bosonization, boundary conformal field theory, and density-matrix renormalization group simulations, we find that a chiral fixed point with maximally asymmetric spin conductance arises at a critical point separating a regime of disconnected chains from a spin-only version of the three-channel Kondo effect. We argue that networks of spin-chain Y junctions provide a controllable approach to construct long-sought chiral spin liquid phases.Introduction.-The spin-1/2 Heisenberg chain represents an analytically accessible model of basic importance in condensed matter theory [1]. By now, many experimental and theoretical works have contributed to a rather complete understanding of this model, including the effects of boundaries and junctions of two chains [2]. However, little attention has been devoted to quantum junctions formed by more than two Heisenberg chains. In fact, recent theoretical developments provide hints that interesting physics should be expected in that direction: First, multichannel Kondo fixed points have been predicted for junctions of anisotropic spin chains [3][4][5][6]. Second, electronic charge transport through junctions of three quantum wires is governed by a variety of nontrivial fixed points which cannot be realized in two-terminal setups [7][8][9][10][11][12][13][14][15][16]. As spin currents in antiferromagnets can be induced by spin pumping [17] or by the longitudinal spin-Seebeck effect [18], it is both an experimentally relevant and fundamental question to determine nontrivial fixed points governing spin transport in junctions of multiple spin chains. In particular, we are interested in the possibility of realizing a circulator for spin currents. While circulators have been discussed for photons [19][20][21] and for quantum Hall edge states [22,23], we are not aware of existing proposals for spin circulators. Once realized, a spin circulator has immediate applications in the field of spintronics [24], which has recently turned to the study of charge-insulating antiferromagnetic materials [25][26][27].In this paper, we study Y junctions of spin-1/2 Heisenberg chains coupled at their ends by spin-rotation [SU(2)] invariant interactions. We assume identical chains such that the junction is Z 3 -symmetric under a cyclic exchange. These conditions are respected by a chiral three-spin coupling J χ [see Eq. (1) below], which breaks time reversal (T ) symmetry and can be tuned from weak to strong coupling, e.g., by changing an Aharonov-Bohm flux [28][29][30]. Apart from condensed matter systems, such Y junctions can also be studied in ultracold atom platforms [31], where Heisenberg chains [32-34] and multi-spin exchange processes [35] have recently been realized. We use three complementary theoretical ap-

Chiral Y junction of quantum spin chains

“…Thus, one should keep in mind that the results may be affected by logarithmic corrections due to the marginal operator in (7). Nonetheless, as we discuss below, we find remarkably good agreement with the analytical predictions that neglect logarithmic corrections as well as with our previous DMRG results [39] for three-spin correlations in the model with J 2 = J c 2 . In figure 5, we show the expectation value of the SSCO at positions j = 1 and j = 2 as a function of J χ for a Y junction with length L = 60.…”

“…Remarkably, this projected Hamiltonian has an emergent time-reversal symmetry since it only contains two-spin (exchange) interactions. However, time-reversal symmetry breaking perturbations appear in the effective Hamiltonian to leading order in J 1 /J χ once we take into account virtual transitions to the excited states of H B [39]. We note that the coupling J K between the central spin S 0 and the new boundary spins of the chains is suppressed by a factor 1/3 in comparison with the bulk exchange coupling.…”

“…In [39], as J χ is varied, we have argued for the phase diagram shown in figure 2. First, we note that the fixed point of where the constant C is constrained to C = 0 or C = ± √ π by virtue of SU (2) invariance, is stable for |J χ | below a critical value J c χ .…”

“…Some results for the chiral Y junction of spin chains obtained using the algorithm proposed in [99] have already been presented in [39]. The method of [99] works efficiently for a Y junction with boundary interaction among spins at the first site, j = 1 and open boundary conditions at j = L. Here, we apply a different numerical scheme especially tailored for the calculation of the spin conductance, described in [83,84].…”

“…In this method, we implement the geometry illustrated in figure 3, featuring two Y junctions facing each other, where the system size (the length of each chain) is finite and one junction is a mirror image of the other. Implementing this geometry with the method used in [39] is equivalent to considering periodic boundary conditions and would require a much higher computational effort. Instead, we treat the double Y junction by mapping the system to a chain with long-range interactions and employing ordinary DMRG as shown schematically in figure 4.…”