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We investigate the ground state phase diagram of the S=1/2 two-leg $XXZ$ spinladder system with an isotropic interchain coupling. In this model, there isthe Berezinskii-Kosterlitz-Thouless transition which occurs at the XY-Haldaneand the XY-rung singlet phase boundaries. It was difficult to determine thetransition line using traditional methods. We overcome this difficulty usingthe level spectroscopy method combined with the twisted boundary conditionmethod, and we check the consistency. We find out that the phase boundarybetween XY phase and Haldane phase lies on the $\Delta=0$ line. And we showthat there exist two different XY phases, which we can distinguishinvestigating a $XX$ correlation function

physical review. b, condensed matter and materials physics

Phase diagram of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">S</mml:mi><mml:mo>=</mml:mo><mml:mstyle scriptlevel="1"><mml:mfrac bevelled="false"><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:mstyle></mml:mrow></mml:math>two-leg<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>X</mml:mi><mml:mi>X</mml:mi><mml:mi>Z</mml:mi></mml:mrow></mml:math>spin-ladder systems

Phase diagram ofS=12two-legXXZspin-ladder systems