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Dear Satrio,
<div>first of all I would like to remember that the posting guidelines invite you to sign your posts with your full affiliation.</div>
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<div>Regarding your question:</div>
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<div>The Hamiltionian in real space IS Hermitian. Probably, you are comparing H(m,n)[R] with H(n,m)[R]. Instead, the correct relationship for the Hamiltonian to be Hermitian is</div>
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<div>H(m,n)[R] = H(n,m)[-R]*</div>
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<div>because the complex-conjugate elements must refer to the same pair of Wannier functions. To understand this better, remember that </div>
<div>H(m,n)[R] is the matrix element between a Wannier function in position </div>
<div>r_m</div>
<div>and Wannier function in position </div>
<div>r_n + R</div>
<div>therefore if you just fix R, and invert m with n, you are not looking at the same pair anymore; you have instead to also invert the sign of R.</div>
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<div>Best,</div>
<div>Giovanni</div>
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<div><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; font-size: medium; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; font-size: medium; ">
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<div>-- </div>
<div>Giovanni Pizzi<br>
Post-doctoral Research Scientist<br>
EPFL STI IMX THEOS<br>
MXC 340 (Bātiment MXC)<br>
Station 12<br>
CH-1015 Lausanne (Switzerland)<br>
Phone: +41 21 69 31124<br>
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<div>On 27 Dec 2013, at 07:05, satrio wrote:</div>
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<div dir="ltr">Dear All
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<div>I have generated hr_plot for single layer MoS2. I found something that i cannot understand. It seems the hamiltonian in real space is not hermitian. For the same distance, the Hij is not conjugate of Hji. Im not sure what cause this as i know the Hamiltonian
should be hermitian. Is there anyone know about this issue?</div>
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<div>Regards</div>
<div>Satrio</div>
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