Conversation between two people involves subtle nonverbal coordination in addition to speech. However, the precise parameters and timing of this coordination remain unclear, which limits our ability to theorize about the neural and cognitive mechanisms of social coordination. In particular, it is unclear if conversation is dominated by synchronization (with no time lag), rapid and reactive mimicry (with lags under 1 s) or traditionally observed mimicry (with several seconds lag), each of which demands a different neural mechanism. Here we describe data from high-resolution motion capture of the head movements of pairs of participants (n = 31 dyads) engaged in structured conversations. In a preregistered analysis pathway, we calculated the wavelet coherence of head motion within dyads as a measure of their nonverbal coordination and report two novel results. First, lowfrequency coherence (0.2-1.1 Hz) is consistent with traditional observations of mimicry, and modeling shows this behavior is generated by a mechanism with a constant 600 ms lag between leader and follower. This is in line with rapid reactive (rather than predictive or memory-driven) models of mimicry behavior, and could be implemented in mirror neuron systems. Second, we find an unexpected pattern of lower-than-chance coherence between participants, or hypo-coherence, at high frequencies (2.6-6.5 Hz). Exploratory analyses show that this systematic decoupling is driven by fast nodding from the listening member of the dyad, and may be a newly identified social signal. These results provide a step towards the quantification of real-world human behavior in high resolution and provide new insights into the mechanisms of social coordination.

We present a thorough numerical study of the Richardson model with quenched disorder (a fully-connected XX-model with longitudinal random fields). We find that for any g > 0 the eigenstates occupy an exponential number of sites on the unperturbed Fock space but that single-spin observables do not thermalize, as tested by a microcanonical version of the Edwards-Anderson order parameter q > 0. We therefore do not observe MBL in this model. We find a relation between the inverse participation ratio, q and the average Hamming distance L between spin configurations covered by a typical eigenstate for which we conjecture a remarkably simple form for the thermodynamic limit L/N = g 2(1+g) . We also studied the random process defined by the spread of a typical eigenstate on configuration space, highlighting several similarities with hopping on percolated hypercube, a process used to mimic the slow relaxation of spin glasses. A nearby non-integrable model is also considered where delocalization is instead observed, although the presence of a phase transition at infinite temperature is questionable.

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-

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Using the thermodynamic Bethe ansatz, we investigate the topological Kondo model, which describes a set of one-dimensional external wires, pertinently coupled to a central region hosting a set of Majorana bound states. After a short review of the Bethe ansatz solution, we study the system at finite temperature and derive its free energy for arbitrary (even and odd) number of external wires. We then analyse the ground state energy as a function of the number of external wires and of their couplings to the Majorana bound states. Then, we compute, both for small and large temperatures, the entropy of the Majorana degrees of freedom localized within the central region and connected to the external wires. Our exact computation of the impurity entropy provides evidence of the importance of fermion parity symmetry in the realization of the topological Kondo model. Finally, we also obtain the low-temperature behaviour of the specific heat of the Majorana bound states, which provides a signature of the non-Fermi-liquid nature of the strongly coupled fixed point.

The topological Kondo (TK) model has been proposed in solid-state quantum devices as a way to realize non-Fermi liquid behaviors in a controllable setting. Another motivation behind the TK model proposal is the demand to demonstrate the quantum dynamical properties of Majorana fermions, which are at the heart of their potential use in topological quantum computation. Here we consider a junction of crossed Tonks-Girardeau gases arranged in a star-geometry (forming a Y-junction), and we perform a theoretical analysis of this system showing that it provides a physical realization of the TK model in the realm of cold atom systems. Using computer-generated holography, we experimentally implement a Y-junction suitable for atom trapping, with controllable and independent parameters. The junction and the transverse size of the atom waveguides are of the order of 5 μm, leading to favorable estimates for the Kondo temperature and for the coupling across the junction. Since our results show that all the required theoretical and experimental ingredients are available, this provides the demonstration of an ultracold atom device that may in principle exhibit the TK effect.

We study a Y junction of spin-1/2 Heisenberg chains with an interaction that breaks both time-reversal and chain exchange symmetries, but not their product nor SU(2) symmetry. The boundary phase diagram features a stable disconnected fixed point at weak coupling and a stable three-channel Kondo fixed point at strong coupling, separated by an unstable chiral fixed point at intermediate coupling. Using non-abelian bosonization and boundary conformal field theory, together with density matrix renormalization group and quantum Monte Carlo simulations, we characterize the signatures of these low-energy fixed points. In particular, we address the boundary entropy, the spin conductance, and the temperature dependence of the scalar spin chirality and the magnetic susceptibility at the boundary. h B n d Q h w Z Q E P A M r / D m P D o v z r v z M W 8 t O P n M I f y B 8 / k D h C + P n A = = < / l a t e x i t > J < l a t e x i t s h a 1 _ b a s e 6 4 = " 1 I Z Z 6 U M H d 4 D 0 X 9 s v v f d t 9 + 0 / G f o = " > A A A B 7 X i c d V D L S s N A F J 3 U V 6 2 v q k s 3 g 0 V w F Z I Y 2 r o r u h F X F e w D 2 l A m 0 0 k 7 d j I T Z i Z C C f 0 H N y 4 U c e v / u P N v n L Q V V P T A h c M 5 9 3 L v P W H C q N K O 8 2 E V V l b X 1 j e K m 6 W t 7 Z 3 d v f L + Q V u J V G L S w o I J 2 Q 2 R I o x y 0 t J U M 9 J N J E F x y E g n n F z m f u e e S E U F v 9 X T h A Q x G n E a U Y y 0 k d r X g z 4 e 0 0 G 5 4 t j n 9 a r n V 6 F j O 0 7 N 9 d y c e D X / z I e u U X J U w B L N Q f m 9 P x Q 4 j Q n X m C G l e q 6 T 6 C B D U l P M y K z U T x V J E J 6 g E e k Z y l F M V J D N r 5 3 B E 6 M M Y S S k K a 7 h X P 0 + k a F Y q W k c m s 4 Y 6 b H 6 7 e X i X 1 4 v 1 V E 9 y C h P U k 0 4 X i y K U g a 1 g P n r c E g l w Z p N D U F Y U n M r x G M k E d Y m o J I J 4 e t T + D 9 p e 7 b r 2 O 6 N X 2 l c L O M o g i N w D E 6 B C 2 q g A a 5 A E 7 Q A B n f g A T y B Z 0 t Y j 9 a L 9 b p o L V j L m U P w A 9 b b J 6 z A j z E = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " 1 I Z Z 6 U M H d 4 D 0 X 9 s v v f d t 9 + 0 / G f o = " > A A A B 7 X i c d V D L S s N A F J 3 U V 6 2 v q k s 3 g 0 V w F Z I Y 2 r o r u h F X F e w D 2 l A m 0 0 k 7 d j I T Z i Z C C f 0 H N y 4 U c e v / u P N v n L Q V V P T A h c M 5 9 3 L v P W H C q N K O 8 2 E V V l b X 1 j e K m 6 W t 7 Z 3 d v f L + Q V u J V G L S w o I J 2 Q 2 R I o x y 0 t J U M 9 J N J E F x y E g n n F z m f u e e S E U F v 9 X T h A Q x G n E a U Y y 0 k d r X g z 4 e 0 0 G 5 4 t j n 9 a r n V 6 F j O 0 7 N 9 d y c e D X / z I e u U X J U w B L N Q f m 9 P x Q 4 j Q n X m C G l e q 6 T 6 C B D U l P M y K z U T x V J E J 6 g E e k Z y l F M V J D N r 5 3 B E 6 M M Y S S k K a 7 h X P 0 + k a F Y q W k c m s 4 Y 6 b H 6 7 e X i X 1 4 v 1 V E 9 y C h P U k 0 4 X i y K U g a 1 g P n r c E g l w Z p N D U F Y U n M r x G M k E d Y m o J I J 4 e t T + D 9 p e 7 b r 2 O 6 N X 2 l c L O M o g i N w D E 6 B C 2 q g A a 5 A E 7 Q A B n f g A T y B Z 0 t Y j 9 a L 9 b p o L V j L m U P w A 9 b b J 6 z A j z E = < / l a t e x i t > < l a t e x i t s ...

We study the finite-temperature expectation values of exponential fields in the sine-Gordon model. Using finite-volume regularization, we give a low-temperature expansion of such quantities in terms of the connected diagonal matrix elements, for which we provide explicit formulas. For special values of the exponent, computations by other methods are available and used to validate our findings. Our results can also be interpreted as a further support for a previous conjecture about the connection between finite-and infinite-volume form factors valid up to terms exponentially decaying in the volume.